The given equation of a line is,

The above equation can be rewritten as,

The general equation of a line in slope-intercept form is given by,

Here, m is the slope of the line and c is the y intercept.
Comparing equations (1) and (2), we get slope m=5.
We have to find the equation of a line parallel to the given line 5x-y=-3 and passing through point (x1, y1)=(-3,2).
The slopes of two parallel lines are always equal. Hence, the slope of a line parallel to 5x-y=-3 is m=5.
Now, the point-slope form of a line with slope m=5 and passing through point (x1, y1)=(-3,2) can be written as,

Rearrange the above equation in slope intercept form.

Therefore, the equation of a line parallel to the given line 5x-y=-3 and passing through point (-3,2) is y=5x+17.