As noted elsewhere my experience of the 5070 is that it will only boot in UEFI mode, not Legacy mode. I followed a similar path to what I did with the Wyse 3040 and checked out Puppy Linux and the 32-bit and 64-bit versions of Tiny Core 12.0 all of which ran without any problems.
The onboard flash appears as /dev/mmcblk0.
UEFI booting describes how I installed Tiny Core to the internal eMMC flash of the 5070.
Any comments? email me. Added July 2021