I just have to clarify something here.
The designations like "T5", "T8", and "T12" do NOT specify any particular type of fixture. They only speak to the bulb sizes and shapes. The "T" refers to a tubular bulb and that means ANY bulb that has a tubular shape. And the numbers refer to the number of eights of an inch those bulbs measure. So a "12" bulb is 12/8" in diameter or 1.5". The "8" bulbs are 8/8" in diameter or just plain 1". And the "5" bulbs are 5/8" in diameter. That's IT. That is ALL those designations say or imply. Nothing more.
They do not say anything about the length of the bulb. They do not say anything about the type of base or contacts or even wires that the bulb may have for connections. They do not even say anything about WHERE that base or those contacts maybe on the bulb. A bulb that is tubular with a 1" diameter and a 6" length and that has a bayonet base mounted 1/3 of the way down that 6" length, on the side would still be a "T8" bulb. Other features can be added to the bulbs or bases and those designations would still hold.
The T8 and T12 fluorescent bulbs in common use have been engineered to use different ballasts (for the most part). So a fixture sold with a ballast designed for a T12 bulb is referred to as a T12 fixture. BUT, if you are going to install LED bulbs that do not use those old ballasts, then a T8 LED bulb will fit equally well in a T8 or a T12 fixture and will work just fine there after you remove or wire around the ballast in those fixtures. I have several dozen T8 LED bulbs that are installed and working in fixtures that were made long before the idea of a T8 fluorescent bulb was even dreamed of. They work just fine. The original T12 SOCKETS were used for the T8 bulbs when they were designed so a T8 bulb will fit in a T12 fixture and vice-versa.
The T5 fluorescent bulbs in general use use a different pin spacing so they will not fit in the T8 and T12 fixtures unless the sockets are changed. The stated advantage of T5 bulbs and fixtures is that they are not as thick as the older, T8 and T12 fixtures, "providing more room for racks or shelving".
So I am wondering just what kind of bulbs are you planning to use in these T5 fixtures. Or what you are trying to accomplish? Are you really that short of vertical space?
If it is a quality thing, light or the fixtures, let me say this. My shop is small. I had installed those inexpensive fluorescent "shop lights" sold at home supply places for around $20 each. They gave me nothing but trouble with fluorescent bulbs: weak light, bulbs blinking off and on, etc. I purchased T8 sized, LED bulbs that could work without ballasts and installed them that way. My shop is lit like the sun: no dark corners or bad spots. With the same number of bulbs, in the same fixtures, in the exact same places, I easily have twice the light. It is great. And it has remained that way for about three years now. Not a single problem: they JUST WORK!. And this is with the original, $20 fixtures and the original sockets. Only the bulbs were changed.
With over 45 years of experience at work and several years in my shop, fluorescent bulbs SUCK! LED bulbs are GREAT!