City sight-seeing:
TST promenade/Avenue of Stars. Be there at 8pm for the nightly laser show
The Peak
If you travel down the island, take the tram at least once. Especially good if you can get a seat in the front on the top floor.
People will say star ferry but I think it's gross. Lots of pollution on the harbour, and combined with the waves you will probably be sick the rest of the day
Nan Lian Garden (Diamond Hill) and Chi Lin Nunnery next to it
Must see: Hong Kong Museum of History (if you are interested in HK culture itself). Free on Wednesdays. If you have never been to HK before, it might be a good idea to go here first, then you'll have context for the rest of your trip
Touristy shopping for crap: Stanley market, Ladies Market (Mong Kok), Temple Street Market (Jordan)
You can spend half a day easy in MK checking out all the different areas... Starting at Prince Edward you can see the goldfish area, fa yuen street market (cheap clothes, toys, etc. Good deals here if you do't care about brand), bird market, flower market, , etc, and some fantastic restaurants.
Outdoorsy stuff/walking: Mui Wo (rent a bike), Tai O (stay in a fishing village)
Go check out the horse races at Happy Valley or Sha Tin
Go to Sai Kung for a walk and for seafood. Or go to the very end and rent a BBQ pit (all you can eat IIRC)
Make a day trip to Macau, if you like casinos. The food is one of a kind - highly recommend Fernando's on Hak Sa beach (very south). Watch a show like Cirque or see if there are any concerts
You can probably do ALL that in 5 days I think. For more info: GOOGLE