No.
The standard aquarium industry 48" light fixture will handle T8 bulbs. Older units will only run T12 bulbs.
Since you wrote you didn't want HO, you can replace the ballast and sockets, to run one or two T5NO (normal output) lamps. They don't get too hot for the plastic the fixture is made of.
If you had asked about T5HO, I'd have warned that T5HO (high output) lamps normally come in metal fixtures with metal reflectors and often have cooling fans.
If you were located in Japan or Europe, you might be able to find adapters that would allow you to use T5 in a T8 fixture. They were available there when the governments mandated more efficient lighting to save building more power plants.