iMessage problems

Ok. I have an iPhone 5s and when I had my 4s ( 2 weeks ago before I switched to my 5s) when I would text one of my contacts, it would send as iMessage but wouldn't say "Delivered", it would just sit there. But if I text my other contacts that have iPhones, it goes through perfectly fine. I've restarted my phone by holding the power button and home button, I've turned iMessage on then back on, and I've signed out of my Apple ID and signed back in. I don't know if it's on the other contacts end or not. Please help?