Really, you shouldn't need to shower after 5 miles. Just moderate your pace, especially in the last half mile or so to cool down. If you really feel you must, then a quick wipe over the sweatiest bits with baby wipes will do fine - you can do that in a toilet cubicle.
Wearing cycling wear designed to 'wick' sweat away from your body will probably help, although I just wear a t-shirt and either craghoppers or jeans depending on which job I'm going to - in other words, I wear my normal work clothes. Nearly everyone I know cycles to work, in normal clothes, and none of them shower when they get there.
Don't let the the lack of a shower get in the way of cycling. This idea that you have to shower after the slightest effort is just tosh, and one of the things that make people think they can't cycle to work. (or at least, gives them an excuse not to).
I know what you are saying, and have started doing that on cooler days... but the last 3 miles of the journey is all uphill, with the final section being particularly steep (there is a quarter mile with a steady 15% climb at one point). Not a lady-like thing to admit, but I do seem to sweat an above average amount. If you were the person sitting next to me, you would probably agree that I do need a shower after 5 miles.
It doesn't help that I work in a hot office with rubbish air conditioning, so I sit there all day, roasting, and feeling like I'm stinking the place out. I have been thinking that I might get less hot if I moved the stuff in my rucksack into panniers, and I guess the cooler weather will make a difference.
Also, I alternate running and cycling, so cycle in, run home, run in, cycle home, etc, so really do need a shower on running days. I sometimes cycle the long (18 mile) way round, so again, would definitely rather shower after that.
I guess if I was told that I was no longer allowed to use the men's showers, I could happily not shower, guilt free...But since I have that option, I feel like I have to sure it for the sake of everyone else! I wouldn't let it stop me from cycling to work, but it is starting to make me hate it a bit.