I am slightly confused about how far a PC can jump in combat. On page 182, the PHB defines the mechanics of the long jump:
When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
The subsequent description of the high jump is essentially analogous with the Strength score replaced with the Strength modifier. However, it also features the following addition:
In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
Since this is explicitly spelled out for the high jump and no similar mechanic is mentioned in the context of the long jump, I'd be inclined to infer that being able to jump farther by making a successful Strength check is not intended by the game designers. However, on page 175, the PHB explicitly lists the following as an example of an Athletics check:
You try to jump an unusually long distance
Note though, that it is not specified whether this pertains to horizontal or vertical distances, so it could be that this is just a re-iteration of the above-mentioned rule about high jumps. Given the vocabulary used in the distinction between long (horizontal) and high (vertical) jumps, it seems reasonable to assume that this sentence is talking about a horizontal distance, though. Still, there is no explicit mention of exceeding your normal maximum length for a long jump.
Unlike in this discussion, I do not care about whether or not it is possible to split up the jump over several rounds. For the sake of simplicity, let us only talk about crossing a horizontal gap that is longer than your Strength score but shorter than your Movement minus a 10 feet start. Let's use the (vague) nomenclature in the PHB and call a jump over such a distance an unusually long jump. My question then is:
Is it, by RAW, indeed possible to perform an unusually long jump by passing a Strength (Athletics) check?
I have the following context in mind: When playing on a grid, the relevant jump lengths are usually multiples of 5 feet. If for example a PC has a Strength score of 8, that effectively means they can jump only 5 feet. In my opinion, letting them jump 10 feet instead should obviously not come for free, but it also shouldn't be too big a deal. If someone could refer me to an official source that offers clarification on that matter, I'd be very happy. Maybe some rule book even features a table for suitable DCs for given jump lengths. I know that this exists in DnD 3.5, so maybe there is hope for 5e as well.
Best Answer
1. Is it possible to exceed your normal maximum jump length by passing a Strength (Athletics) check?
This is a bit situational. Say, for example, a PC only has a Strength Score of 5. If there is a 10 ft gap, and if the player cannot make it, it's death. If we use the rule for a long jump, the PC is going to die.
But, this rule about a long jump is what the PC is normally capable of doing. A PC with a strength score of 5 is perfectly capable of jumping 5ft without exerting extra effort. The rules for using an ability check states (emphasis mine):
In this situation, jumping beyond the PC's innate ability is possible, but uncertain. Therefore, a Strength Ability check to jump twice the distance is required.
Alternatively, the DM could use a Passive Check instead, which gives an innate +10 to their ability check, without a dice roll; but the catch is that this is normally used for abilites that are repeated on a regular basis. In this case, if the PC has had plenty of practice jumping long distances, they could use a Passive Check to jump the distance.
Ability and Passive Ability checks don't work the same way as the "Long Jump" rule, that calculates a total potential distance that a person is capable of jumping; instead they work in a "pass/fail" manner to see whether or not the PC is capable of clearing the entire obstacle. This could be translated back into a distance after the roll, if you wish (e.g. the DC to pass was 15, the PC got a 14 over all, so they just barely failed), in which case you could say that they didn't clear the jump, instead falling short by a foot instead.
2. If so, is there a guideline for the DC of jumping a given number of feet farther than one's Strength score?
As far as I'm aware, there isn't a distance:difficulty ratio or table, but the basic rules again do provide a table of typical difficulty classes. This situation would have to be determined by the DM as to how difficult the jump would be.
In this case, I believe that a 10ft long jump would likely be somewhere between easy and medium (a DC of 10 to 15). For example, a PC with a strength score of 10 could do this naturally (by following the innate rules of a long jump with a 10 foot run up). A PC with a Strength score of 5 has a -3 modifier. The challenge of the jump is far more difficult for them, therefore needing a higher roll (minimum of 13 on the dice) to pass.
3. Would such an unusually long jump still be simply a part of one's Movement, or would it consume an action? Would it maybe cost extra feet of Movement?
As the rules state (as you provided in your question) (emphasis mine):
In this situation, you are making a long jump. This is part of your movement, however difficult it might be. The reason they dictate this as part of your movement is that yes, you can move and attack at the same time, but you can only move a specific amount of distance on your turn - this is the speed you can cover normally cover in a 6-second time frame (e.g. 30 feet, without using the Dash Action).
So, if the PC has moved 10 feet, then needs a 10 foot run up, and then must cover another 10 feet in your jump, that is as much movement as they are able to traverse in their move.
Using this (very basic) example, moving into a square requires 5 ft of movement. So, moving into the first square containing the obstacle requires 5 ft of movement, then moving into the second square requires another 5 ft of movement. Technically, passing this obstacle, which by definition of the grid, is only 10 ft wide, technically requires 15 ft of movement to pass the obstacle completely. So, you could manage this in 2 ways:
In 5e, the rule of thumb with rounding is usually to round down. When applying this to your grid however, it's understandable to round to the nearest 5 ft that represents as success. I.e. if they have passed the jump, they are placed in the square past the obstacle; or if the have failed, they are placed on the square of the obstacle. Using a grid is a tool to help identify distances physically, in a relative or rounded manner.
You could alternatively place them on the same square as the obstacle, and simply mark them as "safe" (standing up) or "unsafe" (lying down) to indicate a pass or fail respectively, if you want to keep to the "rounding down" rule of thumb used throughout the rest of the 5e system.