I've got a trip with my family in a couple of weeks for 5 days to TPE. This is my wife/daughter's first trip, but I've been there plenty of times. 5 days will pretty much restrict me to Taipei and the immediate vicinity. If you want to see all of Taiwan, you'll need at least 2 weeks.

Of course this is all going to depend on budget, what your interests are and how comfortable you are in areas where English might not be widely spoken.