My baby is almost 5 months old and has been sleeping on his side. Is it ok for him to still be in bassinet ? Or should I transition him into his cot where there is more room?

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 

Yes, he does need to be moved to his cot now, & for swaddling to be ceased. (if not already)
Babies been the space of a cot & arms free to roll well.
Ensure mattress is firm & flat & nothing soft or loose in his cot.
Continue to always place your baby on back for sleep.

Is he able to roll & change his position during sleep?
How does he go with tummy time when awake?
Increasing tummy time when awake is important to build upper body strength to roll well (both ways)
This might mean increasing frequency of tummy time, rather than how long he is on his tummy each time.
Is he rolling from tummy/side to back during tummy time, holding his head well &/or reaching for toys?