Hi,
I remember feeling very very inadequate when my baby was 5 weeks old, too. She was also a frequent eater, her sleep pattern was all over the place and was very irregular. To be honest, she is now 19 months old and is still unpredictable regarding sleep, she is a spirited baby when it comes to sleep. So I know how you feel. Hugs!
First of all, is your son eating so frequently since he was born or is it something that started recently? If it started recently he may be going through a growth spurt when he is basically working on increasing your milk supply. If that's the case, go with a flow, let him nurse often, this will pass in a few days.
If he has been like this from the birth, I would say that he just likes to nurse for comfort. Babies don't know how to calm down, put themselves to sleep, and relax on their own, they need our help. The easiest for a newborn is to suck to release his stress, tiredness and whatever else. A new mom usually has problems to distinquish hungry cries from tired or bored cries and everytime offers her breast. I was doing that for quite a long time, everytime my dd cried, she was nursed. Anyway, in those first weeks it is so hard to know what to do, especially when you are sleep deprived and you just want your baby happy and have some rest yourself. And I am not saying that is wrong, but if you feel exhausted and want to try something else, I can understand you.
One thing that can help you to make sure that your baby is getting more milk at a time is to do breast compressions, you need to squeeze your breast when your baby starts to slow down, more info:
http://www.thebirthden.com/Newman.html (you need to click on the link about breast compression).
Some other thing to try is to offer a pacifier if he has just fed and you think he just needs to suck. But do this only if you are sure he is not in a growth spurt at that moment, which usually happens at 5.5-6 weeks.
How is he sleeping? If you tell us more we will be able to help better.