The reason that your credit score will drop five to 10 points is due to the hard inquiry on your credit report (when a lender pulls your credit). A hard inquiry is one of the factors that impact your score the least, comprising about 10% of your total credit score. Credit bureaus also allow you to get as many hard inquiries as you want in a 14-day period and it only counts as one, so if you’re shopping around, make sure to do so within this window.
As you continue to make your car loan payments on time, you should find that your credit score rises. After about a year or two, depending on the credit bureau, the hard inquiry will fall off your credit report altogether, giving you a strong credit score.