I recently bought a replacement mattress from Clark Rubber for our bassinet (as we bought a second hand one). It was custom cut foam as the bassinet is an odd size. The foam is 5cm thick - is this a safe thickness for a bassinet mattress? Just wondering as its about double the thickness of the mattress that came in the bassinet.

As there are no mandatory standards for bassinets in Australia, Red Nose recommends the guidelines from Product Safety when looking to use a bassinet for the first few months.
Also, baby should be moved to a cot once they are showing signs of rolling.
https://rednose.org.au/article/bassinettes

These recommendations include:

Ensure the sides of the bassinette are at least 300 mm higher than the top of the mattress base.
Ensure it has a wide stable base and a sturdy bottom so that it won’t tip over.
Ensure the mattress fits well and is firm, smooth and no more than 75 mm thick.
If the product has folding legs, make sure it cannot accidentally fold during use.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/bassinettes