For which prime numbers p is the quotient ring $\displaystyle F_5[x]/(x^2+1)$ a field?

From theorems in my notes, I know this quotient ring is a field if $\displaystyle (x^2+1)$ is a maximal ideal, i.e $\displaystyle (x^2+1)$ is irreducible modulo p over the field $\displaystyle F_5[x]$.

I don't see where to go from here though.. any help would be great

Thank you!