Answer
Yes, even, plus sign
Work Step by Step
We have an entry from each column and each row thus it is a determinant of order $5$.
The ordered pairs that are out of order are(if we swap $a_{32}$ and $a_{24}$ it is easier to see it): $(4,2),(4,3),(5,4),(3,2)$, thus the number of inversions is $2$, the parity is even, thus the sign is positive.
