5 weeks is not enough time. Keep going. Meanwhile, read this pinned post: http://talk.collegeconfidential.com/college-life/2016222-to-those-who-feel-lonely-homesick-friendless-think-they-chose-the-wrong-school-etc-p1.html
You will be home for the holidays soon. You like you r college, you like your classes and you have friends. Stop dwelling on the non-permanance of your situation. You aren’t being ripped from your home and family. They will always be there for you. There are many anti-anxiety techniques you can try to help you cope with those feelings. Keep going to counseling because it’s not going to hurt you. You can also see a doctor and find out if maybe anti-anxiety medicine might be a good idea. Leaving a college that you claim you really like just doesn’t seem very sensible. I do think if you leave to go to the local community college, that may not make you happy either.