I just opened an iPhone 5 for the second time. I agree, opening is the hardest part. If you don't have good luck with the suction cup method, you might resort to the razor blade method which I found way easier. It does leave a little scratch mark along the joint but any case covers it. Look up YouTube jammed SIM card removal. https://m.youtube.com/watch?v=Z8m-O93gaX...
My battery was loose! It had been held only with very thin two sided tape. The phone is a refurb but I don't think the battery had been replaced because it is worn out just 6 months later.