iPhone 5 on silent mode still makes noise

Dear iPhone users,

It could be that I am overlooking something completely, but I'm experiencing problems with putting the iPhone 5 on silent mode.

When I use the switch on the side I can clearly see the phone being put to silent (crossed out bell). When I receive phone calls I don't hear my ringtone and it goes to vibrate like it should be... When I receive texts however the phone just plays the normal text-message ringtone.

I really need the phone be silent and vibrating for all incoming notifications when I put it on silent. Otherwise I need to shut down my phone while I'm working or in school...

Thanks in advance!