For an experiment on the effect of a buffer solution, I need to calculate the expected pH of the buffer.

I know that I have to make an amounts table and use the Hasselbalch equation to find the pH.

For the first part, 0.10M HCl was added to a buffer. The first addition was 5 mL of the HCl.

Before doing the amounts table I know I have to find moles of HCl.
So 0.10M X 0.005 = 0.0005. Did I do this correctly?

yes

Yes, you have calculated the moles of HCl correctly.

To find the moles of HCl, you multiply the concentration of HCl (0.10 M) by the volume of HCl added (0.005 L or 5 mL converted to liters).

So, 0.10 M x 0.005 L = 0.0005 moles of HCl.

This is the correct amount of moles of HCl added to the buffer solution.