Hi- trainee midwife here. Congrats on your baby!
Do you mean that your baby is sleeping for a total of 5 hours in 24? This is not a normal sleeping pattern for a newborn. While babies do differ, a 2 week old breastfed baby should be spending most of their time asleep, waking mainly for feeds. Feeding is likely to be very frequent, between every 1 and 3 hours, and could take between 40 mins to an hour for each feed. So for example, if your baby feeds around every 1.5 hours and takes an hour to finish a feed, this could be both normal and also feel pretty continuous! Babies also feed for closeness and it is common for newborns to only want to sleep on the breast. Look up the 4th trimester.
A better indicator is how your baby behaves when awake or immediately after a feed. Does he/she seem unsettled most of the time? A 2 week old should be having at least 6 soaking nappies a day, as well as dirty ones. Is the weight gain ok? How does feeding feel for your wife. Is it comfortable or painful? What do her instincts tell her? Does she think something is wrong?
I think you need some face to face breastfeeding support from a Lactation consultant asap. There could be something like a tongue tie or a problem with the baby's latch that means baby is not transferring milk effectively. By all means speak to your community midwife, but be aware that not all midwives are as knowledgable about breastfeeding as they should be. A Lactation consultant is an expert and will be able to spot any problems.
Of course you may introduce a bottle if you choose, it's your baby! If your wife is able to express with a pump, you could do some feeds to give her a break and let her rest. If she struggles to express, or simply doesn't want to then formula is an option. Just be aware that in the early days baby needs to go to the breast frequently to maintain supply, supplementing with formula disrupts the balance and might mean that her supply suffers later down the line. However an occasional bottle shouldn't be a problem. Another thing to be aware of is the possibility of nipple confusion, where baby rejects the breast in favour of the bottle.
Carrying the baby in a sling is a good way to calm him/her if they're fussy, but definitely do get some breastfeeding support as what you mention doesn't sound entirely normal to me.
Good luck!