Why is there only 3 constitutional isomers of pentane (C5H12)?

Isomers are the possible different structures of pentane (C5H12). It is too small to have a greater variety of isomers.

Try drawing out the possible structures for pentane and you will find only one chain of 5 carbons (with the hydrogens attached so that no carbon has more than 4 bonds)

C-C-C-C-C-C

It is possible to draw a 4 carbon chain with a single carbon branch off one side

C-C-C-C l C but you cannot put the extra carbon on the end or you'll just have a chain of 5 again. Putting the extra carbon on the second gives the same structure as putting the extra carbon on the 3rd position.

A 3 carbon chain is also possible

C l C-C-C l C

There are no other possilbe arrangements as no other arrangements would be new.