To simplify the given expression, we first need to find the vectors AB, BC, and AC.

Let's assume that A, B, and C are three points in 3-dimensional space, and vectors AB, BC, and AC can be represented as follows:

AB = B - A
BC = C - B
AC = C - A

Now, we can substitute these vectors into the given expression:

-5/2(AB + BC - 1/2AC)
= -5/2(B - A + C - B - 1/2(C - A))
= -5/2(B - A + C - B - 1/2C + 1/2A)
= -5/2(-1/2C + 1/2A + 1/2C - B + C - B)
= -5/2(1/2A - 2B + 3/2C)

Therefore, the simplified form of the expression is -5/4A + 5B - 15/4C.