They go away. The spell gives you a loan of 5 current HP and 5 max HP, and when the spell ends, you give 5 max HP and 5 current HP back.

(Maybe they intended you to keep the current HP like in other healing spells, but I'd be hard put to reason that the "for the duration" somehow makes the maximum HP temporary, but not the current HP too. We've also little indication this was a mistake, other than it's surprising. So, let's go by what they wrote.)

That can drop you to 0hp, but by the end of the 8 hours, you're probably resting and in a healthy state, and the loss of a portion of your HP won't be devastating.

The fact it can drop you to 0hp might be surprising, but it makes sense from the spell's description:

Your spell bolsters your allies with toughness and resolve.

The spell gives you a little bit of extra oomph to keep you going. (Well, eight hours of oomph.) When the spell goes away, that oomph does too. If you're decently healthy, you'll feel slightly more worn. If you're at 1-4hp, basically on the brink of passing out and dying, then this oomph is the little bit extra that's still keeping you going, and it will be bad if it goes away.

Have healing spells handy if you have someone under Aid, and keep track of time to make sure they're in a healthy state when it ends.

Of course, if you find the above absurd or terrible or something else, you can feel free to say the 5hp granted goes away first, just like temporary HP.

Isn't it Temporary HP?

Probably not. D&D 5e does have rules for Temporary Hit Points, but this spell doesn't appear to grant them. They could have written "temporary HP", but instead they wrote "current HP".

The argument could be made they should be interpreted as Temporary HP because they're temporary, but nothing in either Aid's description nor the writing about Temporary HP really suggests this interpretation should be made. Aid seems to grant real HP, which means it can do things Temporary HP can't do, like bring you back from 0hp.

The bless spell is not interrupted

The key to the answer is:

You briefly stop the flow of time for everyone but yourself.

For everyone else, delta t is zero.

No time passes for other creatures

Turns / rounds each last six seconds -- six seconds elapse from the beginning of someone's turn and the beginning of their next turn. From this game mechanic, we can say that the usual delta t from round to round is six seconds. Spells with duration of a minute can be modeled as being on a counter in this case: you count down one for each turn/round elapsed.

For everyone who is not the archmage, their time / turn / round counter remains where it was when time stop went into effect. Since no time is passing for them, the durations of their spells are, compared to the archmage's frame of reference, extended. The archmage's delta t keeps moving. For the other characters, they don't notice a difference since for them time stopped.

The bless spell's duration depends on the caster

In the case of bless, a concentration spell, the duration is keyed to the character who cast it, which is also the character who is concentrating on it. If it is a character who is not the archmage, their delta t is zero so their duration counter resumes on their next turn. (That is after time stop ends). Their spell still lasts a minute for them because time (and the counter) stopped for everyone but the archmage. That would provide the archmage with a few extra rounds / turns of the bless spell's magical effects.

If the archmage cast bless (from a ring of spell storing) it's duration would keep decreasing since time/turns are ticking away for the archmage.

@Medix2 asked for clarification in a comment:

If bless were cast by somebody else, but cast on the Archmage, would they benefit from it?

The answer is: yes. Nothing in the time stop spell says that it stops the effects of other spells. Bless, once it takes effect, keeps on taking effect until the spell ends (or concentration ends). Nothing in its text says otherwise.

Concentration
Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends. (Basic Rules p. 79)

In plain English, you in those two sentences is the caster of a spell requiring concentration. Unless you lose concentration, the spell does not end.