Question 972372
log5 (5^x-5)= x-5

log to the base of something of the same something =1.  log to the base of something of the same something raised to the power is the power.  Here it is in numerical form:

log10 10=1
ln e=1
log 10 (10^2)=2   ;;  log (100)=2

log5 5^3=log5 125=3

You can also put the exponent out in front.

log5 5^(x-5)=
(x-5) log5 (5)=x-5