Hi, sorry to hear about your injury. Yes, in my experience (fractured T8 six and a half years ago) 5 weeks isn't that far into your recovery. Admittedly, I was never given a back brace (didn't even know such things existed until it was far too late!) and it turned out I had undiagnosed osteoporosis, so my recovery was prolonged. However, even with healthy bone density and a brace, you should expect at least 8 weeks before you begin to recover more energy and have noticeably less pain. Unfortunately, though the vertebra will heal magnificently as long as you're careful, the surrounding muscles will be traumatised for a while yet, and that (as you're probably aware) is the real battle when healing from a spinal fracture.
I found the anxiety very challenging. With hindsight I'd suggest coaching yourself out of fearful catastrophic thoughts about 'what it all means'. I think culturally we have quite a fearful complex about broken backs and necks - you only have to notice some people's expressions when you tell them you've broken your back! But essentially it's just another broken bone, and it heals with time and you'll get back most if not all of its previous functionality. So take heart. I wasn't a particularly active person back then (am more so since, because it gave me a jolt) but the realisation of how fundamental to basic activity and mobility that injury was did haunt me for a while. In a sense, we grieve for the 'healthy spine' and that can be difficult to go through.
Try to see this period as an enforced justification to watch lots of telly or read or write or learn a new skill that doesn't require much if any physicality. Search youtube for guided meditations for dealing with pain and anxiety too, there's some great stuff on there. I found tapping helped a lot with my anxiety (search youtube for 'tapping for anxiety'), and Mark Williams' Mindfulness book and CD.
Your body is channeling much of your energy into healing at the moment, so you will feel very tired for a while and even small chores will take it out of you. But that'll improve and pass as the coming weeks go by. Since it's almost that time of year, try not to expect too much of your body but focus on getting to Christmas Day and noticing then how much difference the next 3 weeks will have made. Allow yourself to ask for and/or accept help and support from whoever's around you, too. This isn't a 'normal' phase of your life, but you will get back to normal when your body is ready, so focus on accepting that. For very active people, that can be challenging. But you're up to it, I bet! 