$$\sum_{j=1}^{546}\left[ \frac{(5j)}{(1093)}\right ]$$
Where the brackets are the floor function. I'm not even sure how to start this question besides just figuring out for how many numbers the floor of the function equates to 0, 1, 2, etc by trial and error.
First, note that
$$0<\frac{5j}{1093}<1$$
leads to
$$0<5j<1093$$
which in turn leads to
$$0<j<218.6$$
This tells us that all $j$ from $1$ to $218$ will produce a summand of $0$
Now, do the same thing for
$$1<\frac{5j}{1093}<2$$
and find those $j$ that will give a summand of 1 for each $j$... rinse and repeat until you've gotten to your upper bound of 546...