Without thinking, I've previously connected it to my FTDI interface with 5V outputs and it worked fine, but only now realised it should have been done with level shift resistors.
I'm guessing there are input protection resistors?
Just about to connect SEROUT output to a 5V PIC device, and if it doesn't work directly - the PIC has a Schmitt on its UART input, so probably won't - will have to use a level shifter. It's not possible to run the PIC on 3.3V this time as there's an LCD in use that must run from 5V