A binary operation ⊗ is defined on the set of integers such that m⊗n = m + n + mn for all integers m and n. The identity element for this operation is an element e such that m⊗e = e⊗m = m for all integers m. Since the identity element is given to be 0, we have:

m⊗0 = m + 0 + m x 0 = m

So, 0 is indeed the identity element for this operation.

The inverse of an element m under a binary operation with identity element e is an element n such that m⊗n = n⊗m = e. In this case, we want to find the inverse of -5 under the given operation with identity element 0. Let n be the inverse of -5. Then, we have:

-5⊗n = -5 + n + (-5) x n = 0

Solving this equation for n, we get:

-5 + n - 5n = 0

-5n + n = 5

-4n = 5

n = -5/4

So, the inverse of -5 under the given operation with identity element 0 is -5/4.