The number of functions defined from {1, 2, 3, 4, 5} ⟶ {a, b} which are one-one is:

If we consider one-one function, only two elements of the set $\{1,2,3,4,5\}$ can have images.
Therefore, there can't be a one-one function from  $\{1,2,3,4,5\}\to \{a,b\}$
Hence, the number of one-one functions is 0 .