I have this issue. Played the same video, on the same WiFi connection on the youTube app on my 4 and 5.. The 4 played instantly and loaded faster than it played. The 5 is basically unwatchable. Took about 10 second to start, then played about 3 seconds, buffered for 20, then played a few more, then repeat... Strange thing is I turn off WiFi and switch to 4G (non LTE) and it plays fast. Although, it looks like youTube drops the video quality when on 4G.
Although, I did the same with the iTunes Fesitval app which provides very high quality video and they both play instantly and smoothly on WiFi. So, I'd guess this is a youTube issue.
I did a speed tst on my WiFi and it gets like 17 mbps so I don't think I have the slow WiFi issue reported by other 5 users.
So basically the exact same issue the OP has...