Here we can make coefficients of x and y in, both equations, equal to each other and then apply,
Perpendicular Distance =
( | c1 - c2 | ) / √(a²+ b²)
Here by taking "2" common in second equation, it becomes
5x - 12y -39/2 = 0
Applying the above formula for 5x-12y+65= 0 and 5x - 12y -39/2 = 0, we get
Distance = (65+39/2) / √(5² + 12²)
= (169/2)/13 = 13/2 units....