There are four polyominoes, one of each size 1-4, in the 4x4 grid below. They have been placed so that none of them are able to slide inside the grid.

+--+--+--+--+
| 3  3|     |
+  +--+  +  +
| 3| 2|     |
+--+  +--+--+
|  | 2| 4  4|
+  +--+  +--+
|  | 4  4| 1|
+--+--+--+--+

Place five polyominoes, one of each size 1-5, in a 6x6 grid so that none of them can slide.
Similarily place six polyominoes, one of each size 1-6, in an 8x8 grid.

Note, the polyominoes can be any valid shape of connected squares for each size. The size 3 piece used may be either the L shape or the straight shape. There are 5 possible shapes for the size 4 piece, 12 for the size 5 piece, and 35 for the size 6 piece.

Extra: Does a solution for the 4 pieces in a 4x4 grid exist for each of the size 4 pieces?
Does a solution for the 5 pieces in a 6x6 grid exist for each of the size 5 pieces?