As for Taekwondo's earliest gyms, you mean original 2 Kwans, Changmugwan & Pasaenggwan. From my sources, everyone learned Gwonbub from YMCA Gwonbub club (1946) & Chosunyeonmugwan Gwonbub Club. Even the Taekwondo people who called their art Toudi/Tangsu by linguistic influence learned from Byungin Yoon, according to my sources. Also, there should be physical evidences for YMCA Gwonbub club (1946) & Chosunyeonmugwan Gwonbub Club, paperwork & whatnot.
There are no videos to post on Taekwondo origin. There are photos, writings, screenshots.
What did 5 original Taekwondo Gwan say? That they learned Karate? No, according to my sources, they all learned Gwonbub. Korean Gwonbub 300 years ago looks different from Kung Fu & looks similar to today's Taekwondo & Karate because Karate probably copied it in 1922. Also, I don't see anything about 5 original Taekwondo Gwans saying about Karate other than that they sometimes called Taekwondo Tangsu/Toudi, which is from linguistic influence. I can't find "we learned Karate" from Korean Taekwondo gyms created after YMCA Gwonbub Club.