There are two ways to get the image on the sd-card.
If you start from a Windows pc you can use the 'Raspberry Pi Imager' to get the image on the sd-card.
For Linux and a Mac you can use the dd command.
On Wikipedia you can find a table of all 'B' models with 64-bit processor indication field.
For the RPi Pico, RPi Zero and others you have to read the applicable text for more details.
On the forum there is a section where you can find the piCore release information.
Here you can find for example that support of RPi5 was introduced in piCore 14.1 for 64-bit only.
The current latest piCore 15.0 has better support of the RPi5.
The next release is not far from now, so watch the forum.
The following link details the steps using the dd command.