Hi
I just wanted to say that I felt exactly the same at 5 weeks, it was summer time too and we were just hot, sticky and bothered all of the time. I came to dread every feed and I had none of the problems you list - except that i could never master feeding lying down either - it got easier for me once I was able to really identify what he actually needed (a feed, comfort, sleep etc) so I wasn't constantly feeding him - at five weeks it's so hard to establish whats what, or it was for me. That cut down 'feed' time dramatically and we fell into a routine, it was about me understanding him I think and as you know, that will come.
This isn't for everybody but if it comes down to the point where you're going to give it up, you do have the option to combination feed. We gave a ff as bedtime feed/top up from pretty early on - it really worked for us and took pressure off in all sorts of areas and I used to so look forward to dp taking over just for that one feed. Like I said, it isn't for all, but I felt very similar to you and it helped me carry on.
I found going out difficult so introduced an expressed milk bottle early on. This gave me a break and reduced fear about feeding in public. Also, I would google feeding areas in places where I was headed as a back up plan - john lewis for example are brilliant - m&s a bit crap, and we even got a little tent for beach times! Its all about planning.....and gaining confidence and give yourself a break, 5 weeks is brand new!
My little man is now 6 months and I'm so very pleased I stuck with it, he has started to drop feeds now we're weaning and I'm so sad! I've been really enjoying feeding him since about 16 weeks and I now cherish every feed!
You're doing brilliantly, think how many feeds he's already had the benefit of at 5 weeks.