http://schaken-brabo.blogspot.be/2012/11/de-onzin-van-blitz.html

An article in which I discussed the (non)sense of blitz.
Just one paragraph which I translate:
"Blitz/ bullet have a.f.a.i.k. also an added value for standard chess. You practice tactics, stress-management and you get a good feeling of which positions you do play better. It is also a good tool to test your repertoire. Some grandmasters take online blitz very seriously as I read some time ago that the German grandmaster Falko Bindrich was irritated because moderators took away his +3000 rating on Playchess. This prevented him to play against very strong grandmasters and to improve his repertoire."

I'm not sure how many stupid things Nakamura has to say/claim/do before we can start just discounting what he says. His own dad was his coach and trainer since he was less than five years old. If playing blitz alone helped beyond a certain point then I'd be a grandmaster by now.

And when Nakamura reached that 2300 level, he had played in about 200 USCF tournaments (of all kinds) ...

I think 3-5min blitz games are excellent for practising your opening repertoire and finding any potential gaps in your knowledge. When I first took up the Nimzo-Indian and began practising my repertoire I quickly became accustomed to all the trappy lines White has at his disposal. It's better to fall for them in a 3-5min blitz game where I don't really care about a rating than in an otb game where I do. Therefore I think if you play this fast games as a tool to refine your openings and not as tool for chess improvement it is very worthwhile.

Neither investigating the tree of variations in detail nor  planning intelligently can be done in 10-15 minute games, let alone 5-minute games; yet those skills are what most of chess is. Honestly, if this is most of your experience, you probably have no idea what skilled chess players actually do. Play games at 2 hours+ per game, preferably in person (so you won't worry about cheating), and before every move try to note the important features of the position--all of them--and anticipate everything dangerous that could happen for the next two or three moves--not missing anything. If this sounds like a lot of work, it is; and organizing it in your head, disciplining yourself to do it, suppressing the urge to move until you've completed the necessary investigation, etc. is not trivial.

I'll guarantee you one thing about those strong players who play blitz: they didn't get strong by playing blitz!

Er, "slow chess games" might be considered as something like at least 2 hours per player per game.   

5 minutes per player per game is an old standard for a just-for-fun version, blitz/speed chess.