What am I doing wrong

Question

The original question is logbase5(2x+5)=3. I distributed to get log(base5)2x + log(base5)5. Using the law of logarithms, this would mean that this addition can be made into log(base5)10x by multiplying 2x and 5. This gives you log(base5)10x=3, so you can make 3 an exponent of the base 5 and set that equal to 10x, making it 10x=125. This makes x=12.5, but my answer sheet says 60. What am I doing wrong

Answer 1

The first step is wrong. You could not distribute like that. 

You should live it like that. Just do the following:

2x+5=5³

2x= 125-5

x=60