Aid could use some help
Aid can't really work as written
Each target's hit point maximum and current hit points increase by 5 for the duration.
The hit point maximum increasing by 5 for the duration is easy to understand. The current hp increase not so much, because of the way hp work.
Most values or scores in the game have a permanent base number, which may then be modified by ongoing or continuous effects of specific durations. Calculating the score at any given point is simply a matter of determining which effects are currently in play. This is true for things like ability scores, speed, armor class, etc. For maximum hp, you know the character's base value, and at any given moment it might also be affected by the aid spell (duration 8 hours), draining from an undead (duration until the next long rest), and so forth.
But current hit points aren't like that. Current hp is not a base value to which ongoing continuous affects are applied. Rather, current hp are a running total and when something changes them, it changes them at once and permanently - you don't track the duration of the effect. When you take damage, you remove those hp immediately and they stay gone. When you heal, you add hp at that time and then they stay there. In fact, the Sage Advice Compendium emphasizes how healing is an instantaneous effect, not an effect with a duration that could be dispelled:
Another example: cure wounds instantaneously restores hit points to a creature. Because the spell’s duration is instantaneous, the restoration can’t be later dispelled. And you don’t suddenly lose hit points if you step into an antimagic field!
Thus, to say as aid does, that it increases the current hp 'for the duration' doesn't really make sense - that's not how current hp work. At the start of the duration adding them is easy enough - a target that receives the spell has their current hp increase by five. But suppose they later take damage - does that damage come off of the hp bestowed by aid, or the other ones, or some of each? Are the hp from aid the first ones to be lost or the last ones to be lost as a character takes damage? How could hp come off the ones bestowed by aid, if those hp are supposed last for the duration? If the hp from aid "go away" at the end of the duration, what if they have already been lost?
We can try to make sense of this by saying that aid is a continuous effect that provides a creature with 'five more current hp than they would otherwise have without the spell'. That seems reasonable enough, calculate current hp, with the all the instantaneous additions and subtractions that you normally would, and then at end of your calculations just add five. This 'add five at the end' can be run as a continuous effect that applies for the duration of the spell. This seems like it would work, until we realize the problem of zero.
Suppose a creature has 10 hp and receives aid. Calculate their hp as normal, then add five. They now have 15hp. Good.
Then they take 5 damage. Calculate their hp as normal (10-5 = 5), then add five. They are now at 10hp. Good.
Then they take 7 damage. Calculate their hp as normal (5-7 = 0, by the rules of hp, unconscious and making death saves), then add five. They are now at 5hp. Hmm.
If our rule is that aid is a continuous effect that adds 5 to current hp for 8 hours, a character with aid cannot drop below 5hp.1
So, let's try this. Aid is not a continuous effect. Rather it 'loans' the target 5hp when cast, but 'takes them back' at the end of the duration. Does that work? Well, for one thing that's not how the spell is written, but if it works I'd be willing to forgive that. Unfortunately it doesn't work, either, largely because the 'taking them back' mechanism is not described. If a character was at 10 thanks to aid, at the end of the spell they drop down to 5, easy enough. But what if they are at 3? Even if the spell 'takes its hp back', it can only take back three - what happens to the other two still 'owed?' (another version of the problem of zero). If I am at 0hp but stable when the spell's duration runs out, I can't lose hp, but does the attempt to 'take them back' count as a source of damage? Do I have to start making death saves? Then again, if I am inventing some mechanism by which the spell removes current hp at the end of the duration, what happens if the spell doesn't reach the end of its duration? What if it is dispelled? Do I still have to pay the hp back? If I do, how could the spell take them back if it has been dispelled and is no longer in effect?
Aid cannot work as written because current hp is not a base value to which ongoing continuous affects are applied.
What can we do?
A better model for a version of aid that actually works is provided by the spell heroes' feast. This is an instantaneous spell that provides some immediate benefits (hp gain, cured of diseases and poison), as well as some ongoing effects that persist for 24 hours (immune to poison, being frightened, advantage on Wisdom saves, increase in max hp). Most relevant in that while it provides a continuous effect increase in maximum hp, for current hp it just says that hp are gained, without even calling them current hp.
This is what a functional version of aid would do; treat the change in current hp as a one-time, instantaneous gain, with nothing to be 'paid back' later, but retain the increase in max hp as an ongoing effect for the duration. Personally, I would keep aid as a spell with an 8 hour duration rather than make it an instantaneous spell with a lingering 8 hour effect, as befits a spell of second level that should be capable of being dispelled or suppressed by an anti-magic field (unlike the sixth level heroes' feast).
To answer the question, then, if aid is run in a way that makes sense, there is no change to a target's current hp when the spell ends - unless the drop in max hp requires the current hp to drop to the new, lower, maximum, as the already existing rules about max hp require.
1 This situation is analogous to that of a character being drained of strength by a shadow but wearing gauntlets of ogre power. On every hit, the character's base strength score is dropping, but they are also under a continuous effect from the gauntlets that resets their strength to 19. As another example, a character wearing a headband of intellect and then subject to the lair action of a Dyrrn. Even though they are being drained of intelligence, the headband is a continuous effect that resets their Int to 19. In a similar manner, no matter how many hp one loses, the continuous effect of an aid spell run as written means that one cannot drop below 5hp.