I bought one of the Lie Nielsen 3/16 chisels and like it a lot. Veritas also have the PM-V11® Bench Chisels in 3/16, but that’s even more expensive at $76. They are the only two that I was able to find.
3/16 is ~4,7mm so if you can find one a 5mm Chisel will be close to that though that is an unusual Size i only know Narex has a 5mm, other then that a 4mm or 6mm is far more common and available from any manufacturer.
Or as has been said aswell, in the US you might be able to find one second hand.