It should not. You did not state what platform your on what version of photoshop if you had added system fonts photoshop extensions etc. Your not going to find a solution without providing pertinent information.
Watch the splash screen as PS starts; it lists all the startup subroutines as they execute. It should pinpoint the problem (or at least narrow it down).
I have about the same configuration and PS cold-starts in two seconds or so.
See what twenty-one asked for first.
If you have an enormous collection of fonts, it slows down the launch time. Especially if you have a corrupted font.
Also a retarded video card driver can cause a slow launch.