First race recommendations 5k or 10k

I am looking to sign up for Philly/NJ race/races this fall. The main one I’ve looked at is the rocky run on November 11th. I’ve never done a race before and was potentially looking to a 5k this fall and ideally a 10 k after that? I’ve been looking at a bunch of websites online but it’s a lot so kind of overwhelming so I was wondering if anyone has any recs for beginner runners that they had maybe done or heard of before. I’ve been running like 3-4 miles at this point 3 ish times a week and slowly working my way up with longer distances (could only run like half a mile like two months ago). Also if I sign up for the 10 mile rocky race in November, is that a realistic amount of training time to go from like 3 ish miles to 10? any help is appreciated.