My 5 month old has started rolling back to tummy but isn’t able to roll tummy to back. She keeps rolling over onto her tummy to sleep. Do we leave her like this or move her? She liked to bury her face in the mattress - she is on a new breathable cot mattress. Is this safe?

Most babies will be rolling over by 4- 5 months…...some earlier, some later.                                                                  This is normal as babies grow & become stronger.
Many babies then prefer to sleep on their tummy & some seem to face plant at times,
This is not something that needs to be stopped. It is important to make his environment as safe as possible.

Is she in a cot (not bassinet) now?
Have you stopped wrapping?
How does she go with tummy time while awake?

Ensure that the cot mattress is firm & flat & there is nothing soft or loose in her cot, especially as she is face planting at times.
You can try to turn her face if you see her with face down, but often, like rolling to tummy, babies will just go back to their position of comfort.
What happens if you try to move your baby from her tummy?
Always continue to place baby on back to sleep.

Red Nose has the following general information now that she is rolling.

Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over
Let me know if you have further questions.