It’s probably not as hard as you think. I hope to show you in simple steps how to do this.
(a) First, look at the conditions of the limit. x→-3 means that x is a tiny bit smaller than -3 (more negative than -3) or a bit bigger than -3 (more positive, like -2.9, for example). Now we look at which part of the function f(x) applies to a value of x near -3. So look at the if statements and we see that the first condition is x<-1. Since -3 is less than (more negative than) -1, we can forget about all the other conditions, so we use f(x)=1/x². f(-3)=1/9. When x is near -3, f(x) is near 1/9. So the answer is 1/9.
(b) Here x is near 5. The conditions for f(x) are given in order from the most negative to the most positive. 5 is bigger than 2, the last condition, so we ignore the others and use f(x)=-1/(x-2)². f(5)=-1/(5-2)²=-1/3²=-1/9. So when x is near 5, f(x) is near -1/9, the answer.
(c) x=1.5 puts x between 1 and 2 which is the fourth ‘if’, so f(x)=x+1=2.5. When x is near 1.5, f(x) is near 2.5, so 2.5 is the answer.