The X-pentomino tiles the plane, so that tiling is a good way to start. There are two ways to cut an 8x8 region out of that tiling. If one of the 4 central squares of the 8x8 region has an X centred on it, you get this

19 pentomino solution

or else you get this

20 pentomino solution

The latter can be easily improved by replacing the ones at the edges to give this

16 pentomino solution

A different wat to get the same result is

to take four pentominos from the tiling. These cover a 4x4 area. By using 4 sets of 4, you get this solution.

The X-pentomino tiles the plane, so that tiling is a good way to start. There are two ways to cut an 8x8 region out of that tiling. If one of the 4 central squares of the 8x8 region has an X centred on it, you get this

19 pentomino solution

or else you get this

20 pentomino solution

The latter can be easily improved by replacing the ones at the edges to give this

16 pentomino solution

A different way to get the same result is

to take four pentominos from the tiling. These cover a 4x4 area. By using 4 sets of 4, you get this solution.