First I would put the equation into y = mx + b form.
[tex]5y = - 2x + 12[/tex]
[tex]y = \frac{ - 2}{5} x + \frac{12}{5} [/tex]
The slope of a perpendicular line will be a negative reciprocal of the line it is perpendicular too. The slope for the new equation will be 5/2.
Then we can use the point given to find the y intercept(b).
[tex]5 = \frac{5}{2} (4) + b[/tex]
[tex]5 = 10 + b[/tex]
[tex] - 5 = b[/tex]
Now we can write the final equation.
[tex]y = \frac{5}{2} x - 5[/tex]
