It's still a modified base 4, because the significance of the i'th digit is 4^i, not 5^i.
Edited to add: I'm also not sure whether real-life implementations have -0 as an option. Of course -0 could be normalized to +0, but it might be cheaper not to bother if the sign is applied after the digit selection.
No, balanced ternary, for example, uses {-1, 0, 1}. The system you're discussing is balanced quinary (base 5).
https://en.wikipedia.org/wiki/Signed-digit_representation