Hi Chris - if Crispin won't mind - I will "chip in".
I have found a few things to be extremely important to my nemmie's health:
1) really decent water flow (from power-heads that are 'hidden' away enough, and also high enough up on the side of my tank, to ensure that the nemmie does not get "sucked in"). I have placed my ReSun Waver-15000 and my 2 SEIO's in such a way, that my nemmie get's water flow from at least 3 sides.... I also have a LifeTech power-head (at this stage) that supplies water supply from piping that runs behind my live-rock, which blows a stream of water from right behind my nemmie)...
2) VERY good lighting - I had my nemmie +-10cm below my 1 x 150 watt metal (DIY) halide.... I changed my lighting, to an AquaMedic lighting unit, where the lighting is now +-30cm above my tank.... I moved my nemmie (on it's rock) closer to the metal halide lighting (the unit is SLIGHTLY short for my tank - so the metal halides in the unit is now more concentrated in the centre 2 thirds of my tank...
It took my heteractis magnifica +-10 days to get used to the new lighting and settle in.....
Your light sounds like it MIGHT be ok, bearing in mind that you would require AT LEAST 6 to 8 T5's to produce enough light to assist in the process of photosynthesis in the nemmie's flesh (from the zooxanthellae that lives inside the nemmie)..... What wattage of T5's were you looking at?
3) you will DEFINITELY be required to target feed the nemmie once to twice a week.....
4) You NEED to have the highest quality water possible, for your nemmie. The water quality should be good enough to sustain reef corals..... What skimmer do you have or were you thinking of getting?
All this taken care of, then I would not see why you cannot keep one
Please check that you got all this sorted before you buy a nemmie, and also ensure that the nemmie you buy is really healthy, as a damaged/hurt, sick or too stressed out nemmie will MOST LIKELY die in your tank, a few hours later.