Question 672039
First find the slope of the line given by solving for y:

3x - 5y = -15

-5y = -15 - 3x

divide both sides by -5

y = 3 + {{{3/5}}}x

Slope m is the coefficient of x which is {{{3/5}}}

Since our line is perpendicular to the given line, the slope will be the negative reciprocal of the given slope = {{{-5/3}}}

To find the equation use the formula y - y1 = m(x - x1)

x1 = -3

y1 = 2

y - 2 = {{{-5/3}}}(x - (-3))

y - 2 = {{{-5/3}}}(x + 3)

y - 2 = {{{-5/3}}}x - 5

add 2 to both sides

y = {{{-5/3}}}x - 3

In standar form:

y + {{{5/3}}}x = -3