There is no solution.

log (-x) + log (3) = log (2x-15) 

log[(-x)(3)] = log(2x-15)

log(-3x) = log(2x-15)

Since the logs are equal, what they are the logs
of are also equal:

    -3x = 2x - 15
    -5x = -15
      x = 3 

However when we try to check:

log (-x) + log (3) = log (2x-15)

log(-3) + log(3) = log(2·3 - 15)

log(-3) is undefined. Logs cannot be 
taken of 0 or negative numbers, only of 
positive numbers, so the solution 3 is 
extraneous.

log(-3) + log(3) = log(6-15)

log(-3) + log(3) = log(-9)

There is no solution.

Of course your answer of 5
does not check either, but you
must have solved it wrong to have
gotten 5 instead of 3.

Edwin