Solving the Rubik's Cube Optimally Is NP-Complete

Assuming you mean real life cubes, the most common [1] method to solve anything bigger than 3×3×3 is to first reduce to 3×3×3, then solve as a normal 3×3×3 using outer slice turns. On even-sided cubes, that reduction process is sensitive to a number of so-called "reduction parities", meaning in a nutshell that you might be recreating edges [2] in a configuration that isn't possible/solvable on a 3×3×3. This can't happen with odd cubes, because the center piece on faces and edges disambiguates from the start.

So really, most of what you need to know about solving big cubes is there on a 4×4×4, and not on a 5×5×5. To make it fully pedantry-proof [3], you need to know standard methods for both 4×4×4 and 5×5×5, both of which already require solving a 3×3×3.

[1] There are alternate methods that are actually used for 4 or 5 and don't have the "parity weakness", but they don't scale well enough to anything bigger.

[2] Or, obviously, faces, but in real life reducing faces in a valid configuration is considered a prerequisite.

[3] It kind of depends on who you ask whether or not the reduction methods are "the same" moving from 4×4×4 to 5×5×5. They're a direct extension, but they do involve pieces with no counterpart.