There are only 3 tapes in Episode 5 and they're fairly easy to find (relative to some of the other episodes). The rough locations are:
1. The first tape is in the second major area you explore, in the general vicinity of the cell you started the game at in the very first episode. It's on a bench in the guard area. (Not sure how to describe it very specifically, but it's easy to spot while you're working your way around that area...if you chose to follow Mirelle's path, it's generally in between the 2nd and 3rd computers you need to hack).
2. The second tape is the easiest to find. When you get to the atrium, go up the stairs, and right before the door which leads to the next main quest task (the door is marked by a cross on your map), the tape is sitting on the edge of the balcony overlooking the atrium.
3. Instead of following the main quest through the door for tape #2, head back downstairs and through the door toward the Pre-Cal sleeping areas (you need to thoroughly explore this area if you want to get the various collecting achievements). Work your way through this entire section, past the kitchen, and toward the guard barracks. On the first floor of the guard barracks there is a prison cell (where you can get put if spotted/captured). The third tape is in this cell room (outside the cell itself).
You need to actually listen to each tape, which is one by just clicking on it in your inventory (assuming you've got the portable tape player from episode 3).