Some of the math may get a little tedious in this problem. Let me make a recommendation. Once you write down the density of states expression, substitute the expression x*N for the number of defects n, where x is the fractional number of defects n/N. Then simplify the expression that way, and indeed a lot of simplification should happen.
In the rest of the problem, keep things in terms of x, rather than E or n, to keep things easy. You can still take the energy derivative in a pretty easy way. Since x = n/N = E/(epsilon*N) you can express d/dE of something as just 1/(epsilon*N) * d/dx of that something.
And yes, there are two problem 5s. Just seeing if you were paying attention. :)
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