Simple Past is good if you're not at university studying English anymore. If you are still there and still studying English, you would use the perfect progressive and say '... I entered university, where I've been studying English for five years."
The thing I have against your sentence is the use of 'master' where mastering a language is the result of study, so you don't 'master English for five years', rather 'master English in five years/after five years of study'. Your sentence is better as something like 'I entered university where I studied English for five years before mastering it." (or something along those lines)
(not a teacher, just a language lover)
Interested in Language