Combine 8x8 square grid and 15x15 square grid into 17x17 square

Question

You have an $8\times8$ square grid and a $15\times15$ square grid. You want to dissect them and combine them into a $17\times17$ square. What is the minimum number of pieces required?

Only cuts along grid lines are allowed. All pieces be polyominoes.

Answer 1

Here is a solution where the number of pieces is

5.

I believe that fewer pieces is not possible, but do not have proof. Here are some observations that might lead to a proof:

The 4 corners of the 17x17 square must come from four different pieces. Suppose there were only 4 pieces, one in each corner. All the squares along any side of the 17x17 square must come from the two pieces at the nearest corners because the other two corners are too far away. The 8x8 is too small to provide two pieces that cover a complete side. Therefore pieces from the 15x15 must cover two diagonally opposite corners of the final 17x17.