(a) Look at the graph first and you can see it's continuous over the range. The value of the quantity 5-x becomes 5-2=3, so we look at the point on the graph for h(3) and we can see the value is 1, so h(3)=1 and h(3) approaches 1 for values of x close to 2, that is, 5-x close to 3.
(b) h(3+x) becomes h(3) when x approaches 0, and we already know from (a) that h(3)=1, so we have 1-1=0. So the limit as x approaches zero is 0. In this case, the limits don't present any problems, because the graph is continuous, and there are no strange things happening around any of the points within range of the function h as shown.