Field $\mathbb{Z}/5\mathbb{Z}$ means set of integers modulo 5 i.e. this field is $\{0,1,2,3,4\}$.
So vector over this field will contain elements from set $\{0,1,2,3,4\}$ only.
Dimension of each vector is 3 i.e. a vector is a 3-tuple where each element is from $\{0,1,2,3,4\}$.
So for each element in 3-tuple, we have 5 choices, hence total number of vectors is $5*5*5=125$.