I came up with the same answer, but was a little puzzled at mathsyperson's approach. I am always amazed at the different approaches individuals will take. I did it like this.
3ln(-3x+5) = -9 divide by 3
ln(-3x+5) = -3 raise to e
-3x+5 = e^-3 subtract 5
-3x = e^-3 - 5 divide by -3
x = (e^-3 - 5) / -3