What's the solution to 5n+1=5n-1. Please tell me if it's no solution or all real numbers or something else.

5n+1=5n-1 results in

+1 = -1, which is a contradiction

So there is no solution.

(If your variable drops out and you end of with a true statement, then the solution is the set of all real numbers.
If you end up with a false statement, like our case, there is no solution)