There is a good stickerless 5 by 5 speedcube on Amazon for $9.99. There is a even better deal on Amazon including stickerless 5 by 5, 4 by 4, 3 by 3, and 2 by 2 speed cubes.

There are actual centers on this cube, so you don't have to worry about making the centers in the wrong place like the 4 by 4. When you make the centers, they are the center nine pieces, not just 1 piece per side. When you pair the edges, each edge pair is 3 pieces large, and they are the pieces that are on the side not in the corner. The pieces in the corners are corners.

You solve a 5 by 5 just like a 4 by 4. You make the centers. (the center nine pieces on each side) Then, you pair the edges. Pairing edges on a 5 by 5 is different than a 4 by 4, because there is two steps for a 5 by 5 and 1 step for a 4 by 4. (for each edge pair) The last step is to solve it like a 3 by 3. The video might be 2 minutes through so you might have to skip back.

How to solve it: https://www.youtube.com/watch?v=L5CdVJMM-sI

The parity on the 5 by 5 is while you are pairing the edges. In the picture shown, the parity is with the green-orange edge pieces. You can solve this while you are still solving the cube, or at the end. You hold the cube like shown and do this algorithm: (same as 7 by 7 parity algorithm and all R, R', L, and L' moves are with the 2nd layer only from their respective sides) R', U2, L, F2, L', F2, R2, U2, R, U2, R', U2, F2, R2.

P.S. Parity doesn't always have the rest of the cube solved.