Watch this four-part how to video on solving the 5x5 Rubik's Cube Professor. What, you didn't know they made them that big? Well, they do, and it's called the Professor. The 5x5 monolith.
The first step to solving the 5x5 Rubik's Cube is that you need to correctly position the center cubes on each side. Then, you need to finish the center pieces, yes, you're not done yet. The last two centers are the trickiest of the bunch, so be careful. What now? Start pairing the edges, two at a time. This is the most time consuming step of solving the 5x5 Rubik's Cube. Lastly, you need to find out if you have a parity error, by identifying some problematic edges. Then, after fixing all of the problems using the algorithms, you'll be ready to solve it completely, just like a regular Rubik's Cube.
So, get your Cube lubed up, stretch your fingers, and get ready to solve the damn thing. Practice, practice, practice -- then, maybe try some speedcubing, if you're good enough.