No not normal, should only take a minute or two to sync up with iTunes. What type of computer do you use, what version of iTunes do you have? Have you called Apple support? I'm sure someone on here can help you out but you need to give us some more info?
It all depends on what all the above posts have said. What type of computer are you running? , What version of iTunes? etc. If you are using something from a few years back then this sounds about right. When I first got my iPhone I was syncing it with a HP laptop from around 2008 and it was decent, then I moved to my 27" iMac and it is much faster. All that means is that it just depends on what system you are running.