The best I can come up with is 954 feet, with a movement for the round of at least 1040 feet (allowing 10 feet for a run up and some more left over). As a Tabaxi Monk/Barbarian/Rogue/Fighter with Haste, Potion of Storm Giant's Strength and several other spells going at once.
You can nearly treble that again if you decide a Steeder (a giant spider) can wear magic boots, for a total leap of 2754 feet, or just over half a mile.
Basic rules for jumping
In 5e, you can jump a distance equal to your strength score, provided you have a run-up of at least 10ft. But you can't jump further than your movement for the turn. It's a type of movement, not an action.
Effects that increase jumping distance
I found most of these by searching DnDBeyond.com for "jump", or by reading other answers to similar questions on this site and on reddit.
- Potion of Storm Giant Strength sets your strength to 29.
- Jump spell triples your jump distance
- Boots of Springing and Striding also triple your jump distance
- Step of the Wind (Monk 3) doubles your jump distance (and allows you to take a bonus action to dash)
- Remarkable Athlete (Fighter 7) increases your jump distance by your strength modifier
- Second Story Work (Rogue 3) increases your jump distance by your dexterity modifier
- Path of the Totem Warrior with a Tiger spirit (Barbarian 3) increases your jump distance by 10ft
- Wildshape into a female steeder (Dex 16, CR 1, available as a Circle of the Moon Druid from level 2) which has an extraordinary leap ability that effectively triples jumping distance. In fact it's better than that as each foot of movement expended in jumping moves three feet, so if I'm reading it correctly, this isn't capped by speed, as long as the jump distance without the ability is less than the creature's speed for the turn.
Effects that increase movement
- Feline Agility (Tabaxi race) doubles your speed for a turn
- Haste spell doubles your speed
- Boots of Speed doubles your speed
- Using three dash actions (with your action, your bonus action with rogue or monk ability, and the extra action from haste)
- A variety of abilities increase speed (Monk's Unarmored Movement by +10ft at 2nd level up to +30ft at 18th level) Mobile feat +10ft, Longstrider spell, etc)
Most of these effects stack. Lets assume a tabaxi Monk 2/Figher 7/Rogue 3/ Barbarian 3/Something 5, under the effect of a Potion of Storm Giant's Strength.
If "Something" brings monk up to level 6, and adds one level to rogue or barbarian, we get 15ft Unarmored Movement and four ability score increases. We could get more ASI or more Unarmored movement at the expense of the other one depending what classes we take.
With the benefit of four ability score increases on level up, she can use two of them to increase her dexterity to 20 (beginning at 15, +2 from Tabaxi), and one to take the mobile feat.
- Base jump 29 feet from 29 strength score
- +9 from Remarkable Athlete
- +5 from Second Story Work
- +10 from Tiger Spirit in Path of the Totem Warrior
- = 53 feet
- x3 from Jump spell, = 159 feet
- x3 from Boots of Springing and Striding = 477 feet
- x2 from Step of the Wind = 954
- Base 30 feet
- +15 from Unarmored Movement
- +10 from Mobile feat
- +10 from Longstrider spell
- x2 due to Feline Agility = 130
- x2 due to Haste = 260
- x4 due to three Dash actions = 1040
I didn't use the Steeder's jump ability, as I think it can't wear magic boots, and if you have to choose either the Steeder's leap or the Boots of Springing and Striding, you have a slightly better result as a humanoid because you can have dex 20, instead of the default 16 for the Steeder.
For that version, replace three of the five unchosen levels with Druid 3 (Circle of the Moon). Reduce the bonus from Second Story Work from +5 to +3 because of the Steeder's dexterity. You don't need to worry about ASI as you're using the Steeder's physical stats.
Reduce the unarmoured Movement from the Monk to 10ft not 15ft.
I think that gives a jump of 918 feet, in a movement speed of 960 feet, so a little bit left over for the run up. The jump is then tripled due to steeder's ability, without taking up additional movement distance, for a total leap of 2754 feet.
Caveats, quibbles and rules questions
I didn't ensure the character could cast all the spells themselves. If that's a requirement, you'd need the appropriate levels to cast Haste and some of the other spells.
I assumed Jump and Boots of Springing and Striding stack despite having similar effects.
There is never going to be a clear ruling on this. Officially, the same effects (the same magic, or game effects with the same name) don't stack, and everything else does stack. That's fine when there's a limited list of spells and abilities. But in a whole fantasy world, there must be variants, one country has "Jump" spell, and one has "Leap", which gives slightly more distance but has some other downside, and some other country has some other variant of the spell. Do those similar spells stack? It would be better if Jump were written to give a bonus to distance equal to your str score, or similar, so multiple jump spells COULD stack. But that's not the official rules at the moment. And it would still be capped by movement speed.
The athletics skill says it can be used to make leaps that are unusually far or high, but the specific examples cover only height not length. The 3.5e and 4e rules gave the DC for jumping as the distance of the jump, and 5e DCs should be a bit lower as ability scores are limited to a narrower range. But that would only make sense here if all of the extra bonuses were on top of that, because otherwise no character could make the skill DC to jump farther than their base distance, if it has all the bonuses described above.