My 5 month old has started rolling back to front (sometimes without being able to fully remove her arm from under herself) and is persistently rolling onto her tummy to sleep. She hasn't independently rolled from front to back yet. Is it best to continue flipping her back or making sure she's safely on her tummy with arms free before I sleep? I have had trouble sleeping in case she gets stuck but she continues to roll over.

Most babies will be rolling over by 4- 5 months. 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 her new environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

If not already, move baby from bassinet to cot & cease swaddling - babies need arms free & space of cot to roll well & safely.
Continue to always place baby on back for sleep.
Ensure that the cot mattress is firm & flat & there is nothing soft or loose in her cot.

What happens when you roll her back?
Does she stay on her back or roll back to tummy?
How does she go with tummy time when awake? - important to increase tummy time when awake to help strengthen upper body which assists in rolling well.
Let me know, so I can give you more up to date response.
Has she started rolling both ways since your initial email?

Have a look at the Red Nose article linked above (if you haven’t already)