Is $\mathrm{i}$ congruent $2$ or $3$ mod $5$?

Question

The $5$-adic integers contain the $4$-th roots of unity $1$, $\mathrm{i}$, $-1$, and $-\mathrm{i}$. Solving the equations $x^2+1\equiv0\mod{5^k}$ gives two solutions: $\ldots3032431212$ and $\ldots1412013233$. Which of the two is $\mathrm{i}$ and which is $-\mathrm{i}$, if this question does even make sense?