Here we can make coefficients of x and y in, both equations, equal to each other and then apply,

Perpendicular Distance =

( | c_{1 }- c_{2 }| ) / √(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....