Another approach:
There are three variables and one equation.
Therefore if no other restrictions apply, and
if irrational solutions are allowed, then there
are infinitely many solutions for instance.  
n=-2.5, a=.2139968976, b=-2.5
n = -3, a=1, b=-2.097343225

Therefore it is possible only to do one of these
three things:

1. Solve for a in terms on n and b
2. Solve for b in terms of n and a
3. Solve for n in terms of a and b
4. Assume the equation is an identity and holds for all values of n

To avoid infinitely many solutions, I will do only the last.  

Since it must hold for all n, if must hold for n=0, 
so we substitute 0 for n:
  


















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Since it must hold for n=1, we substitute 1 for n, and  for a:
  














Equating exponents of 5



 

Edwin