My 5 month old is in a bassinet in our room. As he is now rolling and moving a lot he ends up with his head in the top corner of the bassinet and face against the mesh. Is this unsafe? The other option is to move him to his cot but that’s our of our room (we do have a monitor) just weighing up which is a safer option.

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 tummy.
This is not something that needs to be stopped. It is important to make his new environment as safe as possible.

It is important to move him to a cot from his bassinet. He needs room to roll safely.
If you are still wrapping him this need to be ceased - he needs his arms free.
Also ensure that the mattress is firm & flat & there is nothing soft or loose in his cot,
Always continue to place baby on back to sleep.

Providing a safe environment takes priority over room sharing.
Parents are not expected to observe baby constantly. If baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered (as baby grows beyond 5-6 months they will move around the cot and roll over; settle baby to sleep on their back but let them find the sleep position they feel most comfortable in.
https://rednose.org.au/article/roomsharing

Red Nose has the following information now that your baby is starting to roll.

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 remain 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