> one dies within 24 hours

Is it really correct to interpret that as "dies in exactly 24 hours"?

Edit: My solution, which assumes that after tasting wine it could take any time between 0 and 24h to die; and that it could vary between tastings:

Given N slaves, you can test 2^N wines in a single iteration, as so:

  - A set of size N has 2**N distinct sub-sets.
  - Have each distinct sub-set taste a different wine.
  - After 24h, everyone who drank the poisoned wine will be dead, and,
    provided you took notes about which set consumed which wine, you
    can look up which wine they drank.
  - (Note also, you leave one wine untasted; if nobody dies, it is the
     poisoned one.)

For our first iteration, we have each set taste multiple wines, like so:

  - The set with five slaves will taste a single wine.
  - Sets with four slaves will taste 2 wines.
  - Sets with three slaves will taste 4 wines.
  - Sets with two slaves will taste 8 wines.
  - Sets with one slave will taste 16 wines.
  - We leave 32 wines untouched.

Of course, in general: a set with N slaves will taste 2^(5 - N) wines.

After 24 hours, all slaves who drank poisoned wine will be dead, and we will have the following possible states:

  - One slave is dead. We know the 16 wines he drank, and we have 4
    slaves left. As shown above, we can easily determine which of
    the 16 wines is poisoned in a single iteration.
  - N slaves are dead. We know which 2**(5-N) wines they drank, and
    we have 5-N slaves left. So we can easily determine which of
    the 2**(5-N) wines is poisoned in a single iteration.

Note that N = 0 is a valid case above.

So, we need to calculate how many wines we can test in this manner. Going through each set:

  - 5 choose 1 * 16 = 80
  - 5 choose 2 * 8 = 80
  - 5 choose 3 * 4 = 40
  - 5 choose 4 * 2 = 10
  - The one wine that all slaves drink the first time.
  - The 32 wines none of them drink the second time.

The sum is 243. Garçon!!! Fetch three more barrels!