jmc

$1<\frac{5}{4}<2$, so the smallest integer greater than or equal to $\frac{5}{4}$ is $2$. Similarly, $-2<-\frac{5}{4}<-1$, so the largest integer less than or equal to $-\frac{5}{4}$ is $-2$. The original expression, $\lceil \frac{5}{4}\rceil +\lfloor -\frac{5}{4}\rfloor$, is equal to the sum of the two, which is just $2+(-2)=\boxed{0}$.