5^(x-3)-5^(x-4)-16*5^(x-5)=2^(x-3)
5(5^(x-5))*(5^((x-3)-(x-5))-5^((x-4)-(x-5))-16*5^((x-5)-(x-5)))=2^(x-3)
(5^(x-5))*(5²-5¹-16*5⁰)=2^(x-3)
(5^(x-5))*(25-5-16)=2^(x-3)
(5^(x-5))*4=2^(x-3) |:4
5^(x-5)=(2^(x-3)):4
5^(x-5)=2^(x-5) |: 2^(x-5)
(5/2)^(x-5)=1
(5/2)^(x-5)=(5/2)⁰
x-5=0
x=5