x=-3 or x=3
Using the property that says :
## ln(a) +ln(b) = ln(a*b)##
We have:
##ln(x-2)+ln(x+2) = ln5##
##ln((x-2)*(x+2)) = ln5##
Rasing exponential both sides we will have:
##(x-2)*(x+2) =5 ##
Applying polynomial property on the equation above that says:
## a^2 – b^2 = (a-b)*(a+b)##
We have: ##(x-2)*(x+2) = x^2-4##
So
##x^2 – 4 = 5 ##
##x^2 – 4 -5 =0##
##x^2 – 9 =0##
##(x-3)*(x+3)=0##
So
##x-3=0## thus ##x=3##
Or
##x+3=0## thus ##x=-3##