First let me get some clarification.
Did you end up mixing with 7ml of sterile water instead of 10? Was the vial of hcg powder or liquid?
If you mixed with a total of 7ml (powdered hcg) then your mixture is 5000/7 = 714iu per ml. A dose of 175iu would be 175/714 or .245 (call it .25) or 25 units on the syringe.
If your hcg was liquid and you mixed that 1 ml with the 7ml, then your mixture is 5000/8 or 625iu per ml. A dose of 175iu would be 175/625 or .28 or 28 units on the syringe.
if neither of these are how you mixed let me know.
A vial of 5000iu at 175iu will last 5000/175 = 28 doses. hcg can start to lose potency after 24 days or so.