A T8 ballast is generally not compatible with a T5 linear fluorescent lamp. These are ratings used to describe the shape and size of fluorescent light bulbs. The T stands for tube shape and 5 or 8 refers to the diameter of the bulb in 1/8 inches. T5 and T8 lamps have different diameters so they are not usually interchangeable. The pin sockets will only line up and complete a circuit in a correctly sized ballast. The exact design of each ballast differs across manufacturers. There are a few ballasts which can be rewired for T5 or T8 bulbs. However, you must still choose a fluorescent bulb of the appropriate nominal length.
Among manufacturer's different product lines, T5 bulbs are usually shorter than T8 bulbs. For example, T5 bulbs may come in nominal lengths from 22 to 58 inches, while all T8 bulbs have a nominal length of 48 inches.
T5 and T8 ballasts are wired for different input powers, ballast factors, and total harmonic distortions. Most ballasts are not designed to be interchangeable and cannot easily be swapped out.