My 5 week old has started to squirm and wriggle a lot in her bassinet, especially towards the end of her naps. She’s not rolling but she ends up moving herself sometimes completely horizontal in the bassinet with her face close to the mesh sides. We have been swaddling her and then tucking her in with a light blanket but now she is squirming she is getting close to under the tucked blanket. Should we move her to sleep sack? Is a tucked blanket no longer safe?

Some babies do not respond well to swaddling & some like their arms free to touch their face or suck on fingers.
Many of these babies will wriggle & squirm in an attempt to get arms free.
Are you using a muslin wrap or a swaddle product?
There are many different types of swaddle suits - but they are all classified as swaddles, ie the baby’s arms are tucked in & not free.
You can try using a muslin or cotton swaddle but wrapping with arms out.
https://rednose.org.au/article/wrapping-babies
In this same link is also some information “wrapping & swaddle products” that you may also find helpful.(scroll down page)

You could also try her in a sleeping bag (arms out)
If she continues to wriggle squirm, you could also try her in her cot.
If there is any risk of the blanket covering her head/face then it may be necessary to stop using.

Have you started tummy time yet?
How does she go? - if you haven’t been doing tummy time yet, it is important to start.
https://rednose.org.au/downloads/RN0407_22_Tummy-Time.pdf

Always continue to place baby on back for sleep.

She may also be getting close to trying to roll.
Most babies are rolling by 4-5 mths - some earlier, some later.