The above drawing shows 1 of the 4 solutions to the problem of tiling a
square with 5 rectangles which have edges in [1,10].

There are 4 solutions, 2 when the square is an 11x11 (see the first link
below), 2 when the square is a 13x13 (see the second link below).

This is the output you get when you run the first program (under Python 3).

G:\>py permutation.py

Solution found:
2 x 10   6 x 1   5 x 8   9 x 3   4 x 7
Solution found:
5 x 10   9 x 1   2 x 8   6 x 3   4 x 7

Python is definitely the language to choose if you are solving this
interesting problem via a computer program. Its iteration tools are
excellent.

http://primepuzzle.com/not.just.tiny.c/permutation.py

http://primepuzzle.com/not.just.tiny.c/permutation_169.py

The programs were written via ChatGPT. Some edits were needed to only
show the solutions that were really different (others came from
rotations and reflections).