Are 5y=15-2x and 2/5x -4 =y perpendicular

No, in order for two pairs of lines to be perpendicular, their slopes need to be opposite and reciprocal. If we divide by 5 to isolate the y on the first one then the slope is -2/5. The slope on the other is 2/5. Yes they are opposites but not reciprocals. So the answer is no.

When 2 lines are perpendicular, they have opposite-reciprocal slopes. This means that they're of the opposite signs and reciprocals of each other.

So start off by putting each equation into slope-intercept form:

5y = 15-2x
y = 3 - 2/5x
y = -2/5x + 3

2/5x-4 = y
y = 2/5x-4

Take the slopes of both lines and compare:
Line 1 >  -2/5
Line 2 >   2/5

The lines do have opposite signs but they're not reciprocals. (If they were, the slopes should've been -2/5 and 5/2). Therefore, NO they're not perpendicular.