That's an inherent property of both the modulus interpretation and the remainder interpretation.

Haskell does it right. Instead of having operators like %, it gives the programmer choice to choose either the modulus or the remainder. Using GP's example:

    ghci> 2 `div` (-5)
    -1
    ghci> 2 `mod` (-5)
    -3

    ghci> 2 `quot` (-5)
    0
    ghci> 2 `rem` (-5)
    2

And we have both (x `quot` y)*y + (x `rem` y) == x and (x `div` y)*y + (x `mod` y) == x