I think any method with identifying symbols on the backs of the cards is likely to fail.
With just 25 symbols, it would be very easy for players to accidentally memorize a telltale clue of one or more of the cards, spoiling the game for themselves, even if they're actively trying not to notice.
I've seen games that try to obfuscate this information by using fluorescent ink revealed by a UV light, or overlapping patterns you need to look at through a coloured filter, so you only clearly see the pattern at the designated "setup" or "check" time, and can't easily use it to track a card throughout play. But for a mystery game like this, leaking that info at setup time is already enough to spoil the puzzle.
What I'd propose instead is a shuffling approach.
Start by laying out the cards face-up, in a 5x5 matrix, with cards of the same taste all in a row, and cards of the same colour in a column. Let's say it looks like...
AV AW AX AY AZ
BV BW BX BY BZ
CV CW CX CY CZ
DV DW DX DY DZ
EV EW EX EY EZ
Turn each card over while keeping it in its place in the matrix. Now the matrix should look like this:
⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜
But the players might still remember which row was which taste, or which column was which colour. So now we'll shuffle them, like a shell game. Slide one row out and move it to one end or the other:
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
Then do the same for a column, and repeat. You can select which row/column to slide each time using a dice roll, rather than leaving it up to the players.
Each time we do one of these shifts, we preserve the fact that each row contains a single taste, and each column contains a single colour, we just switch which one is which in a way that - hopefully, after enough shuffles - your players lose track of.
To make these shuffles easier, you could stack each column into a deck. Then swap the positions of these five decks a few times. Then unpack back to the matrix and stack each row into a deck, and swap the decks around again. You just need to make sure you use the same stacking order in all decks during packing and unpacking (eg. always left-to-right / top-to-bottom). Flipping the order in one deck will make an invalid answer.
Another trick you can use is to have each player take a turn applying a row or column shuffle while the other players are occupied with something else, so no one player can keep track of where every row/column got moved to. This way you can get to complete uncertainty with fewer swaps, where you'd need a higher number to throw off a player with a sharp eye and good memory who can watch the whole process.
After our shuffling, we have a permuted matrix that maybe looks a bit like this, if we looked up from under the glass table:
BX BW BY BV BZ
DX DW DY DV DZ
EX EW EY EV EZ
AX AW AY AV AZ
CX CW CY CV CZ
Now your players choose a random card from the matrix to add to the answer, keeping it face-down so no one sees it. Again you could use dice to make this choice. This leaves us with...
BX BW BY BV BZ Answer: DW
DX DY DV DZ
EX EW EY EV EZ
AX AW AY AV AZ
CX CW CY CV CZ
Now they remove every card in the incomplete row and column and add them to the deck of clues.
BX BY BV BZ Answer: DW
Clues: BW EW AW CW DX DY DV DZ
EX EY EV EZ
AX AY AV AZ
CX CY CV CZ
Slide the remaining cards to return to a square matrix, and repeat:
BX BY BV [BZ] Answer: DW
EX EY EV EZ Clues: BW EW AW CW DX DY DV DZ
AX AY AV AZ
CX CY CV CZ
EX EY EV Answer: DW BZ
AX [AY] AV Clues: BW EW AW CW DX DY DV DZ BX BY BV EZ AZ CZ
CX CY CV
EX EV Answer: DW BZ AY
CX [CV] Clues: BW EW AW CW DX DY DV DZ BX BY BV EZ AZ CZ EY CY AX AV
[EX] Answer: DW BZ AY CV
Clues: BW EW AW CW DX DY DV DZ BX BY BV EZ AZ CZ EY CY AX AV EV CX
Answer: DW BZ AY CV EX
Clues: BW EW AW CW DX DY DV DZ BX BY BV EZ AZ CZ EY CY AX AV EV CX
This procedure ensures you get exactly one of each flavour and one of each colour in the answer pile, and all the remaining cards in the clue pile.
If you find this runs a bit long, you can also abbreviate it. Once you have a shuffled matrix, just take one diagonal into the answer deck and the rest into the clue deck:
[BX] BW BY BV BZ Answer: BX DW EY AV CZ
DX [DW] DY DV DZ Clues: BW BY BV BZ DX DY DV DZ EX EW
EX EW [EY] EV EZ EV EZ AX AW AY AZ CX CW CY CX
AX AW AY [AV] AZ
CX CW CY CV [CZ]
If your initial shuffle was enough to mix up your players' memory of which row/column is which, then this is just as good. But you might find randomizing at the end involves easier manipulations than the row/column shuffling, so splitting your randomizing between the two phases might help the setup phase go quicker.
