243^(.2x)= 81^(x+5)
both 243 and 81 are powers of 3
243 = 3^5 and 81 = 3^4
so rewrite your equation:
243^(.2x)= 81^(x+5)
(3^5)^(.2x) = (3^4)^(x+5)
3^x = 3^(4z+20)
If the bases are the same, for the equation to be true, obviously the exponents have to be the sam
so x = 4x+20
x = -20/3