This is quite clearly a contest problem, meant to be solved by hand and not a computer.  Which also means there is likely some trick, or the right hand side is specially chosen to be solvable.

So lets just use log rules to manipulate the right side:

= log2(2) + log2(5/log2(5))

= 1 + log2(5*log5(2))

= 1 + log2(log5(2^5))

= log5(5) + log2(log5(2^5))

= log5(log2(2^5)) + log2(log5(2^5))

Now the right side is in the same form as the left side.  The answer is now readily seen to be 2^5 = 32.