Proof Writing & Problem Solving · Easy problem

Pólya's advice "try a smaller case first": a $1 \times 1$ grid contains $1$ square, a $2 \times 2$ grid of unit cells contains $5$ squares (four small and one large), and a $3 \times 3$ grid contains $14$. Find the pattern and use it: how many squares of all sizes, with sides along the grid lines, are in a $5 \times 5$ grid?