Log3 (X-5) + log3 (x+3) = 2

LnA + LnB = LnA. B

so we get Log3 (X-5) + log3 (x+3) = Ln3 (x-5) (x+3) = 2 implies

(x-5) (x+3) = 2^3=8, so we can solve easily the quadratic equation

x^2-2x-23=0, there are two solution x=1 - sqrt (24), and x=1+sqrt (24)