let 2^log(5) = x

take log of both sides, we get:

log[2^log(5)] = log(x)

=> log(5)*log(2) = log(x) ................since log(a^b) = blog(a)

=> log(2)*log(5) = log(x)

=> log(5)^log(2) = log(x) ................since blog(a) = log(a^b)

now we can drop the logs, we get

5^log(2) = x

but 2^log(5) = x

=> 5^log(2) = 2^log(5)

if there's anything you don't get, say so