You are given a container with 5 mL of a solution containing 5.1 ×10^3 cells/mL. You are to produce a solution that contains approximately 100 cells/mL.

I really need help solving this problem, it's a serial dilutions problem, but I'm confused about solving it!

If you dilute the solution 10times, like add 50 ml to solution to that 5 ml, then take 1ml, it contains 102 cells/ml

You are given a container with 5 mL of a solution containing 5.1 ×10^3 cells/mL. You are to produce a solution that contains approximately 100 cells/mL.

The solution contains 5.1 ×10^3 cells/mL = 51000 cell/mL and you need to get to 100 cells/mL.
That is a dilution of 51.000/100 = 510 times.

You started with 5 mL solution with 5.1 ×10^3 cells/mL . You need to have a solution with 100 cells/mL.
So what do you need to do than?