Let r" be the actual speed, in mph.

Then the hypothetical speed is (r+13) mph.


Moving at the speed of "r" miles per hour, the car spends  hours.

Traveling with the hypothetical speed, the car would spend  hours.

The condition says

 = 5.


It is your "time" equation.  You must solve it for "r". 
To do it, multiply both sides by the common denominator r*(r+13). You will get

1950*(r+13) - 1950*r = 5r*(r+13),

 = ,

 = 0.

Factor it:

(r+78)*(r-65) = 0.


The only positive root is r = 65.