Short Answer: You can consider the adventures mostly ordered in terms of difficulty as well as character level, but not all of them are "the deadliest in history".
Tales from the Yawning Portal is an excellent book; a collection of some of the great adventures in the history of Dungeons and Dragons. You're looking at a source for seven adventures, all varying in difficulty and length. The promotional description may be a little generalized though. The better description is A collection of exciting and challenging adventures that gives DMs resources for one off adventures for all player levels. Sure, Tome of Horrors are only for DMs looking to eliminate player characters, but the others run differently, and each are challenging in their own way.
The Sunless Citadel and The Forge of Fury are the lowest level, and (relatively) easiest adventures of the book. Citadel is a great one off specifically for 1st level characters. The Forge is perfect as an immediate run right after The Sunless Citadel. These are perfect for teaching new players or those with difficulty with traps on how to handle themselves properly in dungeon crawling. Deadly rating: Not so much. Average difficulty.
The Hidden Shrine of Tamoachan is the next adventure in character level, but definitely takes a climb up in difficulty. Traps are devious. The treasure inside is a little sparse, and may not be worth the danger inside. Even if the players survive the adventure, there is a chance that the dungeon can trap them in, and force them to be new slaves for Tamoachan! Deadly rating: Deadly. Beware.
White Plume Mountain mellows out the challenge a bit, taking an expected challenge for its level range. If the party keeps a level head, the incredibly creative puzzles and environment encounters are not too overwhelming. They are definitely creative, and usually do not take a linear approach like standard traps. So if your players are not used to handling that, it will be difficult! Deadly rating: kinda deadly.
Dead in Thay is really a series of adventures in a super dungeon, and expect this one to compete with Against The Giants for the longest. This one is a collection of very creative "rooms" that all rolled up into a marathon of encounters that will drain your players of their spells and powers per day. Resource Management will be the silent killer in this one. Pay attention to the risk of character death in this place, because if certain conditions are not met, any resurrected character will find their souls trapped forever! Deadly rating: Deadly
Against the Giants is another one that really is multiple adventures. It is three different modules, that will send the players on a tour of the different types of Giants. All of the Giants are dangerous in their own way, so if the players do not adapt their tactics and evaluate their enemies, then they could find themselves in trouble against one type or another. The difficulty evens out for this one though, as it offers some separation between modules, which means a change to rest and recharge - something not readily offered in Dead in Thay Deadly rating: Not so much, Average.
Tomb of Horrors ... Evil. Just ruthless and pure hate. Run this if you promised your players that you would kill some of them. If your players have any trouble with handling traps or figuring out puzzles, it's all but guaranteed to be deadly. There's false entrances that may even be trapped that prevent the party from even entering! Inside, there's a seemingly innocent trap that levitates a player... into a chamber where their only real options are to starve or die of thirst, or run into another room to be assuredly chopped to bits. Then, there is another trap with a chance of being magically stripped of all of your possessions, and then teleported out of the dungeon entirely. Those are just two of the thirty-something encounters of this dungeon. 'Nuff said. Deadly rating: Over 9000. Side effects include: possible rash, intense weeping, may ruin friendships.
I have a fair amount of experience DM'ing for new players, so I'll give my two cents.
No, you won't be able to run a 1st level party through a 3rd-4th level dungeon/adventure
Really, you won't, unless you rebalance everything there to make it proper to 1st level. If you don't intend to spend time doing it, you simply will TPK your party. That's true even for experienced players - the difference between 1st level and 3rd level is very relevant, and a moderate challenge for a 3rd level party can one shot a 1st level party.
It's also not a very good idea to get new players to start at higher levels
Well, to be honest, the alternative is also harsh. Most new players will get confused with only their racial and 1st level features, I usually don't even recommend playing full casters to new players if they don't have time to study how their spellcasting works.
Before adding my solution, I will add some insight on my experience from published adventures, one shots and overall experience with newbie players. If you are not interested, jump to the next line splitting.
The thing with low level adventures
Usually, low level adventures (specifically tier 1 (1-4) and maybe early tier 2 (5-8)) are (quite) large, hard cover adventures for a wide range of levels. Truth is: there isn't many interesting things you can do at low levels. Things start to get interesting around 3rd level (many classes get their signatures there, others get some core features), where a one shot starting at 1st level would be ending. This means it's usually more interesting to level your characters through the entire thing and actually face a Big Bad Evil Guy at higher levels.
The thing with one shots
To actually be one shots, usually they require some experience from the players and the DM (so people don't waste time doing something that has nothing to do with the adventure). For them to be enjoyable, they require even more experience, usually. Finally, since, as I said earlier, early levels aren't exactly amazing and interesting, they are usually designed for higher levels (I'm actually impressed that you found lots of 3rd level one shots, I'm more used to at least tier 2 (5+)). Higher levels, as I mentioned earlier, are most fit for more experienced players.
That said, my sad point is: I really don't feel like D&D (or, at least, 5e) is particuarly suited for one shots for new players. You will learn lots of rules, mechanics and interactions and use it... once. There are a few simpler games that are also, as a whole system, more suited for one shots. I'm not throwing names here because I don't know your (and your party's) tastes for fantasy and whatever else, but chat and forums can help you if you are interested.
Play a 1st level one shot that has enough plot on it
Yes, they exist. Although personally I couldn't finish it in one shot, Death House (from Curse of Strahd), although being a hook (i.e. you should be playing CoS after it, not using it as a one shot) can be played as a one shot. It's designed for 1st to 3rd levels (you level to 3rd level when you finish it though, so it doesn't actually matter, you only play as 1st and 2nd levels). Important note: it's deadly. The main problem I can see with it is that the players, being newbies, will waste too much time and not actually finish it in one (or even two) sessions.
If you search enough, there should be other quick adventures for this same level range though.
Best Answer
I'm showing 21,200 XP if you kill everything.
I've tabulated every hostile creature you would encounter during the adventure by area:
This leaves you 1200 XP short of having a party of four go from 3rd to 5th level. Having read through the module several times, I cannot discern any other stated sources of XP, combat or otherwise.
The Dungeon Master's Guide suggests dispensing non-combat XP at your discretion.
We see in the DMG's section on Experience Points:
This one is up to you. 1200 XP is not a lot of XP, so you should be able to make it up with 2-3 good non-combat challenges somewhere in the module. I won't recommend which, that's for you to figure out.
It is likely the characters are already a little ways into 3rd level.
It seems quite likely that the party didn't start at exactly the XP required to reach 3rd level. Quadratic Wizard pointed out in a comment:
With only 300 XP over the threshhold for 3rd level, simply killing everything will be enough to get the party to 5th.
An understandable miscounting nets an additional 1300 XP, which could explain the discrepancy.
This is getting into educated guess territory, but there were two particular cases where I first miscounted something, and those two cases account for 1300 XP on top of the 21,200, yielding a total of 22,500 XP.
The Wait and Watch section describes two parties of 4 orcs worth 400 XP total arriving two and five days after the player characters. I have included them under Wait and Watch in the table. However, Area 5 mentions them again:
Someone tabulating the total XP available in the module could understandably count both parties in the Wait and Watch section, and then count on of them a second time when reviewing Area 5.
The second mistake I made initially was to double count the gricks encountered in Area 24. They are first mentioned here:
However, they are mentioned again in Area 26, again in a "Creatures" block:
A careful enough reading makes it clear that these are the same gricks mentioned in Area 24, but if I am quickly tabulating XP available, I may miss this and double count them. Each Grick is 450 XP, so counting each of them twice nets another 900 XP.
While XP is not mentioned, it is suggested that training is available in Blasingdell.
In the sidebar "Mining Town of Blasingdell", we read:
So while XP is not mentioned here, it is suggested that some sort of training is available, which could be used to make up for the 1200 XP difference between what is available in the module and what is needed for 5th level.
You can also murder the whole town (or just the important people).
It makes up for the difference, but would probably be a less than agreeable move at most tables.
Conclusion: It's close enough.
Yeah, the raw XP count of the module comes up short of the total XP required for 3rd to 5th, but it shouldn't matter. But there are lots of ways to make up the difference, and the difference isn't large enough for that to be difficult. And if they did make a mistake counting the available XP, it's understandable - I made the same mistake when I first tried tallying things up.