There was a question trying to find a closed form solution for,
$$F(n)=\sum_i^n \lfloor i/5 \rfloor$$
I got that for $n$ in the range $[5 \cdot k-6,5 \cdot k-1]$, where $k$ is a positive natural number, the solution is,
$$F_{[5 \cdot k-6,5 \cdot k-1]}(n)=k \cdot n-{1 \over 2} \cdot (7 \cdot k-5 \cdot k^2)$$
Where the subscript limits the domain of $F$. I don't really care about posting the answer, I'd just like the Op of the question to know the solution. If it helps, I believe Thomas Andrews had a partial answer. Ideally, I'd like this information to be passed on to the Op.