Baby is nearly 5 months old. Started to roll (back to tummy) during wake times and turning 180 degrees while still on back in cot. Tummy time has always been very bad. Unable to tolerate more than a couple of minutes. Worried baby will roll overnight onto tummy and won’t know to turn head to breathe. Unsure what to do besides watching baby all night on a monitor.

Red Nose recommendations are to “always place baby on back for sleep” not baby must always sleep on their back.
https://rednose.org.au/article/red-nose-safe-sleeping-recommendations

Most babies will be rolling over by 4- 5 months. Some earlier, some later.
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side or tummy.
This is not something that needs to be stopped. It is important to make the “new” environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Your baby does need to be in a cot now & also swaddling/wrapping ceased.
Babies been the space of a cot & arms free to roll well.
Ensure mattress is firm & flat & nothing soft or loose in the cot.
Continue to always place your baby on back for sleep.

Is tummy time improving when awake?
Is your baby reaching out for toys as well as having good neck control?
It is important to increase tummy time. If baby does not tolerate longer periods of tummy time try to increase the amount of times per day for tummy time.
Tummy time increases upper body strength necessary for rolling well.

Until baby is rolling well, both ways, try to gently roll baby back, especially when on their tummy during sleep.
No parent is expected to sit up all night watching baby (or the monitor) - this is not sustainable.