Question

A homogeneous linear system in 5 unknowns whose corresponding augmented matrix has a reduced row echelon form with 3 leading 1's will have free variables.

Answer 1

Columns without leading 1's in a reduced row-echelon form of the augmented matrix are called free variables. So, yes it will have 2 free variables corresponding to the two columns without leading 1. In homogeneous system it remains true.