Greetings,
Remove the lens, card and test with a freshly charged battery. If this persists, it looks like the LCD or ribbon cable is failing. I might use this opportunity to upgrade to an R series body, but it won't hurt to see if Canon still services the 5D3 (11 yrs old) and get an estimate.
~Rick
Bay Area - CA
~R5 C (1.0.7.1) ~RF Trinity, ~RF 100 Macro, ~RF 100~400, ~RF 100~500, ~RF 200-800 +RF 1.4x TC, BG-R10, 430EX III-RT ~DxO PhotoLab Elite ~DaVinci Resolve Studio ~ImageClass MF644Cdw/MF656Cdw ~Pixel 8 ~CarePaks Are Worth It
