The connectors at the end of the T5 bulbs are closer together than T8 or T12 bulbs, the fixture will need new end cap things (the part where the bulb attaches to the fixture) and I thought T5s needed a special ballast, but I'm not sure.
And as far as I know 4 foot T5 bulbs don't come in 32 watts, they are 54 for T5HO and 28W for normal output T5.