Since upgrading on October 1, 2015 to Safari 9 in OS X Mavericks 10.9.5 I cannot get 1080p video resolution on YouTube, nothing higher than 720p.

I didn't mean to check that this solved the question, if that is checked it happened inadvertently from the e-mail alert.

I don't have a problem using Firefox--it gets 1080p. And someone who has OS X El Capitan says it works fine for 1080p. Do you also have Mavericks 10.9.5?

Reported to me elsewhere that YouTube 1080p works with his 2013 MacBook Pro with retina using Yosemite and an older 2011 Mac mini with Mavericks. Why not Mavericks 10.9.5. Is this a YouTube problem or Safari problem? It was working before I updated to Safari 9

That should've been the 2013 MacBook Pro with retina was running El Capitan, not Yosemite.

I elaborated on this question on the MacRumors forum; here is what I said, along with a couple other responses, one a suggested work around in addition to your suggestion of reverting to an older versions of Safari, which I'm not sure would work, because in the course of testing with an AppleCare advisor I reinstalled OS X 10.9.5 in a test partition, and it came with Safari 7.0.1, which we then updated (I'd waited a couple of weeks to install Mavericks initially, hence the 7.0.1), but I still was not able to get 1080p on YouTube with Safari 7.0.1. Here is the discourse I mentioned:

I have had the problem since October 1, of Mavericks, in my case OS X 10.9.5, after updating to Safari 9, not being able to play 1080p videos. Starting about 2 or 3 weeks ago, over the course of a week or more I spent about 6 or 7 hours on the phone with AppleCare advisors, including 2 senior advisors, the last one of which followed through with feedback from the engineers to obtain information on the problem. She said my case was the first they were aware this--hard to believe really, but the problem was verified by Apple. The problem affects only Mac OS X 10.9 Mavericks updated to Safari 9; it doesn't affect OS X 10.7, OS X 10.8, OS X 10.10, or OS X 10.11. And the problem is not with flash player, it is with the Media Source Extension (MSE) component of HTML5, which is not functioning. She said they needed to corrected it in a future Safari update but she had no information on when that would be. I have had to use Firefox and set it up with the same shortcuts for convenience as Safari and make it my default browser. By the way, Firefox gets 1080p on YouTube without using flash, as YouTube has switched over to HTML5. The AppleCare advisor said Apple was working with YouTube to correct the problem, but I do not think it is solely with YouTube, as a first-tier advisor initially tested my Safari 9 to see if it would play an animated 1080p trailer generated by Apple, and it wouldn't play that either in 1080p.

Apple released a Safari 9.0.1 update, did that address this issue?

No, the Safari 9.0.1 update did not address the 1080p problem; the AppleCare advisor said it would be a future update but she had no idea of the time frame. All the other versions of OS X from 10.7 to 10.11, except Mavericks, are able to get 1080p, as is Firefox, and they do it without using flash player. The problem is with Media Source Extension not operating in HTML5 through Mavericks. Does anyone know why this might be?

One suggestion was:

to use flash on youtube you can get the safari extension: click to flash, then add youtube.com to the whitelist. it works for me I'm on safari 9.0.1.

By the way, this was a couple weeks ago when the engineers got the log information when I went to YouTube in both Safari and Firefox and became aware of the issue.

PS to my last post: I tried the suggestion of installing the Click to Flash Safari extension, and it didn't work for me in Mavericks 10.9.5. on YouTube.