Had the same problem. Here is my solution:
-Had Final Cut Trial version: Erased it from Apps as the official version will do a fresh install.
-Had iMovie: Why if I liked it i'd use iMovie and not spend 299eur on Final Cut Pro X. Erased iMovie as it is 2.9Gb, with final cut I will never need iMovie IMO
-Removed those Apps I don't need anymore. You know... those apps you only used once for that particular thing at one time or another. If you bought it and need it again it will be available again to download.
Once I was done I cleared at least 5Gb.