Lol no. Days or minutes is a little too much, in my opinion. I feel like there are better things to focus on in a relationship than the exact number of days or how many minutes/hours you've been together. You're wasting time you could be using to make memories.
It seems like something little girls do (12, 13, 14 etc. in their first few relationships). I know a lot of young girls get easily attached to their first few bfs, in an almost obsessed way, these are the girls I assume would count mins or days. The girls that insist on celebrating every week together, or celebrate things like "first time we watched the Simpson's together" or the '7 month anniversary of the first time we held hands in public'.
If you are in a real relationship, you are far too busy enjoying the company of your partner and living life together to count the days. Every day you spend together is so special that the only days you need to make a big deal out of are important ones like 1 year, 2 year, 5 year etc.
I feel like saying '5 months' is a little less creepy than '150 days'.
Personally the worst I've ever been was in my first relationship. We celebrated every month together, with a dinner and a movie. Lol.
Usually people do like keeping a general track of how long they've been in a relationship, but usually in terms of months/years. It would be pretty creepy to keep track of it in terms of days/minutes; I mean you can calculate it from the months/years, but still. There's really no point in doing that.