The solution is
not unique. In the grid below, the 15 and 25 can be entered in the empty spots in either order.
1 12 11 10 9 13 2 23 22 8 14 24 3 21 7 . . 20 4 6 16 17 18 19 5
You can also reverse 21-25 as follows (and then you can still swap 25 and 7):
1 12 11 10 9 13 2 23 24 8 14 22 3 25 7 15 21 20 4 6 16 17 18 19 5