Without knowing the brand and model of switcher, I'm not sure anybody can give a conclusive answer short of making a lucky guess. Personally, I think you're best of consulting a tech support forum.
That being said, 10m is very long for an HDMI cable and while I don't shoehorn Canon's products into neat little boxes, I don't imagine broadcast and long cable configurations were in mind for the 500D/550D. Have you tried using a shorter cable, no more than two metres long?
DSLRs: Canon EOS 7D Mark II, Canon EOS 70D
CSC: Canon EOS M3
Lenses: Canon EF-S 15-85mm f/3.5-5.6 IS USM, EF 50mm f/1.8 II, EF 100-400mm f/4.5-5.6L IS USM, Canon EF-M 18-55mm f/3.5-5.6 IS STM, Canon EF-M 22mm f/2.0 STM