Meredith...this is a TOTALLY normal developmental requirement for a seven week old baby to wake during the night. I would seriously advise that you feed your baby when she wakes during the night and not just give her a paci. As her system matures she will start to sleep longer on her own accord. Each baby is different. Also, just to let you know... 5 hours is considered, medically speaking, as 'sleeping through the night' and many medical practioners don't actually expect babies to be sleeping this long until they are MUCH older.
Cheers
Ted