Enforce the Handle Animal Rules
Getting those dogs to do what they want requires a Handle Animal check (DC 10 and a move action if it's a trick). Each PC can only do that to one animal at a time. Otherwise, the dogs will just generally do whatever you as the DM want them to. That might mean they all swarm something, or it might mean they find the target frightening and run away from it.
Remember, animals will only normally attack other animals, humanoids, monstrous humanoids, and giants. The animal has to be specially trained and use two tricks to have an attack command against anything else.
Kill The Dogs
Unless these are advanced animals with bonus HD, Dogs have 6HP. At 5th level, one Fireball will wipe them all out (the Riding Dogs you gave the party have 13 HP, so their survival chances are better but it should still kill some of them and make the Handle Animal checks harder on the others due to being wounded), and since Dogs are pack animals and one PC can't direct five dogs to attack five different things in one turn, they're likely to not be that far apart.
A Barbarian with Cleave could make short work of them as well. I'm not saying to go far out of your way to kill them, but they're low HP targets in combat, and they make a good target to even the numbers in a fight for certain types of enemies. If none of them are dying in combat at this level, it would be pretty strange.
You could pretty easily make an encounter that would eliminate the dogs in a turn or two, at which point the party will have to decide if it's really worth spending money to buy new ones.
Alternately, you could kill one or two of them in an encounter (which should happen normally in EL 5+ encounters), and see if the party decides that having dogs that aren't up to higher end combat around is a good idea. Any animal lover characters wouldn't want to put animals in harms way that aren't up to it, and the more frugal characters wouldn't want to have something die when they could sell it for gold and get more value out of it.
Initiative Shortcut
When this happens in my game, I roll one initiative for all of a given type (all the Dogs in this case), and have them all move at the same time. That cuts down the annoyance a little bit.
I also don't put much thought into what they're doing. Dogs are animals, not tacticians. They will either do exactly what they're ordered to do, or they'll attack, or they'll not attack. They're not going to get fancy figuring out how to reposition themselves for optimum protection of the PCs. (The PCs would have to use Handle Animal commands to do that.)
As they only have one attack, the rolling should be pretty limited and so you can keep the pace up by acting quickly without thinking about what they're doing.
Party Logistics, As You Mentioned
Is the party carrying enough food for five dogs? Are you enforcing that? Caring for five dogs in real life is actually quite a lot of work, make them deal with that.
This is the kind of thing the DM handwaves away. The rules make it impossible for a creature lacking racial Hit Dice that advances exclusively by level not to have at least 1 level in a class, usually, unfortunately, commoner. Being a level 1 commoner might as well be the same thing as having no combat knowledge; ignoring the orphan's ability scores, the orphan'll be proficient with 1 simple weapon, have 8 skill points, no base attack bonus, no bonus to his saving throws, and all of 2 hp. Because he already exists, though, he does have his starting feat... maybe even two. He remains alive because PCs don't look at him too hard.1
But, with some work, the PCs can turn the little scamp into someone who can contribute. The PCs'll probably have to hold his hand, though, because
Following the Rules as Written to "train" an NPC is extremely dangerous for the NPC
The only rules-as-written thing the PCs can do to "train" the orphan is include the orphan in their adventures. Having the orphan participate in encounters gets the orphan an even share of the encounter's XP value (DMG 36-7), but the DM must rule the orphan participated in the encounter. (Stuffing the orphan into a bag holding when the encounter begins may or may not count.2)
Example
The 4 5th-level PCs and 1 1st-level NPC survive an encounter with 1 Challenge Rating 6 creature. Each of the 4 5th-level PCs earns 450 XP, but the 1st-level 1 NPC earns 540 XP. Another encounter like that takes the 1st-level NPC to level 2!
When the orphan has XP enough to advance a level, the DM makes any decisions about how he gains that level as the DM controls all of the campaign's characters but the PCs. If the DM decides the rambunctious little nitwit continues taking commoner levels, there's really nothing the PCs can do about it except look on in horror.
Persuading the DM: Some Options
Broadly speaking, there are two alternate ways that PCs may persuade the DM that the orphan shouldn't take his next level as commoner. Neither are very good in that the PCs still have no influence over the NPC and both are meant for PCs rather than NPCs. I present them here mainly so they can be disregarded and the DM can simply dispense with this process instead.
Option 1: Make the orphan take the feat Apprentice (DMG2 176)
Upon reaching level 3, the orphan takes this feat, selecting a PC as a mentor. The PC need not have the feat Mentor (DMG2 176), but won't get any of the benefits from being the orphan's mentor if he doesn't. In fact, it's probably funnier if the PC doesn't have the feat Mentor so the kid spends time training around the PC he's selected anyway, copying his moves, vying for his attention, and probably just making a nuisance of himself. That's fine, genre-appropriate, and gives the player an opportunity to assume the grizzled veteran role normally assumed by NPCs.
This is, I admit, an unusual reading of the feat Apprentice, which is intended for PCs rather than NPCs and reading the feat this way requires switching around much of the jargon associated with the description. It doesn't help that the description of the feats Apprentice and Mentor is deeply fiddly, likely to cause frustration and dismay, and goes on for five pages.
I don't recommend this option both because it's a bookkeeping headache and relies on a counterintuitive reading. Further, you'll probably eventually end up--if the DM doesn't handwave it away after reading those rules in the Dungeon Master's Guide II--using the option below anyway.
Option 2: Accompany the orphan on his Rebuilding Quest
The Player's Handbook II describes the processes of Retraining (192-5) and Rebuilding (196-9). These are usually options for players who have made regrettable character choices or want to play something different but want to keep the character's background. Retraining and rebuilding are usually used by high-level characters, but to rebuild one just goes on a DM-designed Rebuild Quest that
should excite and frighten players. It’s an adventure few characters would willingly embark upon and fewer still could survive. To make rebuilding an option at all levels of play, however, the degree of challenge must change according to the PCs’ level. (199)
Luckily, as the orphan is an NPC Commoner 1, the rebuild quest that the DM designs could be pretty short and--from the PCs' perspective--utterly tame. In fact, such a quest could reasonably be an encounter with the PCs.
I don't recommend this route either unless everyone's idea of fun is escorting the NPC scamp as he fights his way through dire rats with his dagger only at the end to emerge battered yet reborn as a 1st-level sorcerer.3
This is, of course, barring shenanigans like taking the commoner-only flaw Chicken Infested (Dragon #330 87) while simultaneously getting the skill Handle Animal to the point where the character rears and trains rocs. But optimizing commoners is an exercise usually better left theoretical.
Although this DM would lean toward may. If a character must expend his actions to keep alive another character, the other character has participated in the encounter, albeit to the party's detriment.
Note that the DM may rule that it's possible for the PCs to create encounters for the NPC. Traps are easiest, with a camouflaged pit trap (CR 1) (DMG 70) costing a weirdly-high-but-nonetheless-affordable 1,800 gp. A commoner who encounters such a trap 3-4 times (not, one hopes, in a row) gains a level. What encountering means in this context I leave to the imagination.
Okay, I admit, that could be fun once. Once.
Best Answer
The simple answer is that there aren't any right now.
The longer answer is that you guys will have to work together as DM and player to figure out what role this creature has in your party, what it can and cannot do in combat and out, and what kind of action expenditure it should require.
The closest similar mechanics we have right now are the Ranger's animal companion mechanics, familiar rules and mounted combat rules. You should review these sections of the PHB (Beast Master Ranger, Find Familiar Spell, Mounted Combat rules) and either decide to model your creature's behavior directly on these rules or come up with a hybrid of the two.