Sliding puzzles can be incredibly difficult to solve, as anyone who's tried can tell you.

Solve the first row and first column first, then the second row and second column, etc.
That's the general stragegy. Think about it: if you have a 5x5 puzzle, solving the first row and first column reduces the problem to a 4x4 puzzle. You will never have to touch that row and column again. You then keep doing that, solving smaller and smaller puzzles until you're done.

To solve the first row, line up all numbers in their proper place except the last two
So, in a 5x5 puzzle, put the 1, 2, and 3 blocks in their proper place. You should have no problem doing this, you wont mess up previous positions.

Put the next number in the top right corner, then the next number below it...