Update my hardware from RPI 4 to RPI 5

I have an RPI4 which has an SSD drive running HA using the recommended startech cable.
I would like to update to an RPI5, is it just a case of boot up the RPI5 off the SSD drive?
Or do I need to install HA onto the RPI5 due to significant hardware changes and what exactly would be my next steps to get everything up again from the RPI4 as I’ve spent 2 years getting my config how I wanted it.

RPI4 gives me problems now with an intermittent ethernet port which dies once a day for a minute and then works again so any advice would be appreciated.

You need to make a full backup of HA and save it on your computer.
Then you will install the image of HAOS for Rpi5 on your ssd with pi imager
After attach your SSD on your Rpi5. Connect USB devices. Boot the Rpi5. wait for the welcome screen and restore your backup file.
It’s not really difficult.