Drying optimization: Leave the bathroom door open and the shower curtain partway pulled so humidity doesn't collect in the room. Have an oversized bath sheet in reach (you can get good ones at Costco). When you're done showering, towel-dry hair, then the rest of you, then comb your hair so it doesn't stick. Without humidity in the room, you don't keep sweating so you don't feel clammy. You can get dressed immediately if you're pressed for time. If you're like me and hate putting dry clothes on damp skin, find something you can do for ~15 minutes at the computer while you air-dry the rest of the way. (ETA: making/eating breakfast is good for this since you probably have to do it anyway.)

(also, I like showers too, but I hate the time lost. I compromised by moving most of my morning routine into the shower, e.g. shaving.)

Edit: And I have no idea how people manage five minute showers. It takes me longer than that just to lather and rinse my hair.