Yes. You absolutely must complete five years residence. The Nationality Act specifies that you must have been in the UK on a day precisely five years before the date of application. If you apply even a couple of days early, you risk having the application refused.
A friend of mine, who has lived in UK for over 20 years, decided to apply for naturalisation a few years ago. Sadly, the date she applied was around the fifth anniversary of her father's death, when she went home for the funeral for just under a week. Her application was refused because she wasn't in UK on the specified day. Expensive mistake....
