If it works well under 2.4 Ghz - but struggles under 5 Ghz - the issue is clearly on your side. Could be a faulty rooter/network adapter (be it malfunctioning, a bad driver/firmware or they're not set properly) or some issue with the ISP - while using the full bandwidth (cause 2.4 Ghz is limited by design).
How's your latency under 2.4 Ghz and 45 Ghz?
Try a simple ping for start, as in...
Press the Windows Key + R (you should get the "Run" tab there) and there copy paste the following:
ping 104.160.131.3 -t
Now observe your latency both using 2.4 Ghz and 5 Ghz (the ping should be constant). Check it for at least 7 minutes - to see if there's any spikes. You could check this as well - to see how the connection in your city while using the current ISP...
https://lagreport.na.leagueoflegends.com/en/#
It's quite likely that all the past complaints on this topic (5 Ghz probing be to be unstable/unreliable while 2.4 Ghz was working fine) - were related to some issue on the user side. As can be seen even in the first topic from google - while searching something like "league of legends lag under 5 ghz..."
http://forums.na.leagueoflegends.com/board/showthread.php?t=4333155
"I've had this issue too, when I took my Sager NP9150 home for the holidays my stepdad has a a rt-ac66u and I would always lag on 5ghz but be perfectly fine on the 2.4ghz. We realized about a month ago that he was running stock firmware (and that the wireless driver on my sager was hideously out of date) It seems that just the firmware update on the router was enough to drastically improve performance, but also the wireless driver update helped a lot too. Have you checked for firmware updates available on the router recently?"