No, I run 5k every day, either on the road or the treadmill, but not necessarily in a race. I have been running a 5k race almost every weekend for the last five months. I live in Orlando, Florida. We'll have plenty of races to choose from every weekend until the summer.
Because I intentionally set my workout run to be 5 kilometers so that it matches an actual road race. Yes, I'm an American and we generally use miles as a distance unit, but the vast majority of our road races are 5ks.
Yes, but there's only a difference of an eighth of a mile -- less than a minute of running -- and you're going against convention. The very fact that someone was confused in the first place should tell you something is wrong saying "5k."
It's a big difference to me when I'm doing my morning run to put in that extra tenth of a mile beyond 3 miles at the end as I'm measuring my time against my PR. Your experience may vary, especially if you run longer distances.