Write the units at every step, because units errors are the failure mode that catches everyone eventually.
Rotation of injection site is a tolerability measure, not a pharmacokinetic one, but if you are going to do it you might as well do it right.
Breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.
Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.
If in doubt, use more diluent and accept the shorter usable window.