Yes, it is possible for the servants to discover which barrel of wine
was poisoned.
The solution is to label each wine barrel with a 5-digit ternary number from
00000 to 22220. Number each servant from 0 to 4. At the beginning, servant `i`
should drink from all wine barrels whose `i`th-most significant digit is 1.
After 24 hours, servant `i` should drink from all wine barrels whose
`i`th digit is 2.
For each `i`, let `k_i` be 0 if the `i`th servant survives, 1 if the `i`th
servant dies within the first 24 hours, and 2 if the `i`th servant dies after
between 24 and 48 hours. Then the poisoned wine bottle is
k_0 k_1 k_2 k_3 k_4.
The problem is possible because we were able to assign unique
5-digit ternary numbers to the wine barrels, since
3^5 = 243 >= 240.
Clearly, this strategy is one instance of a more general one.
In general, let `wineBarrels` be the number of wine barrels, `numServants`
be the number of servants, and `time` be the number of disjoint units of time
available for the servants to test with. Then the poisoned barrel can be
discovered as long as
(time + 1)^numServants >= wineBarrels.