Answer
$(a)$ $(8,5)$
$(b)$ $(a+3, b+2)$
$(c)$ $(0, 2)$
$(d)$
$A(-5, -1)$ => $A'(-2, 1)$
$B(-3, 2)$ => $B'(0, 4)$
$C(2, 1)$ => $C'(5, 3)$
Work Step by Step
Shifting to the right means to increase $x$ value of a point by $3$ units.
Shifting a point upward, means to increase $y$ value by $2$ units.
$(a)$ The point $(5,3)$ will become $(5+3, 3+2)$ => $(8,5)$
$(b)$ Point $(a,b)$ will become $(a+3, b+2)$
$(c)$ To find the point which was shifted by these units, then we have to do the calculation backwards. Instead of increase we have to decrease the $x$ and $y$ values, so we will take the original values of the point.
$(3,4)$ was $(3-3, 4-2)$ => $(0, 2)$
$(d)$ In this case we have to apply the same calculation to each of these points.
$A(-5, -1)$ => $A'(-5+3, -1+2)$ => $A'(-2, 1)$
$B(-3, 2)$ => $B'(-3+3, 2+2)$ => $B'(0, 4)$
$C(2, 1)$ => $C'(2+3, 1+2)$ => $C'(5, 3)$