I'd call 5/0 classic blitz.
OTB, I agree. Online, you do not need to reset the pieces you knocked over, nor press the button on the clock. For me, thus, 3 0 online is closer to 5 0 OTB.
Those old BHB clocks would spin on the table in the donut shop when players were under a minute. One guy glued some foam on the bottom of his to prevent this.
5/0 Losers chess
3/0 wimps chess
1/0 bullet head
I'd call 5/0 classic blitz.
OTB, I agree. Online, you do not need to reset the pieces you knocked over, nor press the button on the clock. For me, thus, 3 0 online is closer to 5 0 OTB.
Those old BHB clocks would spin on the table in the donut shop when players were under a minute. One guy glued some foam on the bottom of his to prevent this.
Yes, you are right, didn't think about it.
I played 10 minute without increment when it was classed as blitz but they changed it so I now play 5/5.
It remained so due to old clocks which didnt have the option of increment. I think increments are a very good option in modern chess.
I'd prefer Bronstein's increment, although I'd find it difficult to get used at this point.
All FIDE competitions are with increment: 90|30, 15|10, 5|3, 3|2.
I play without increments here because the quick pairing formats for the game lengths I like to play do not give me the option. On lichess I always play with increments.
Obviously, it's a matter of taste but I prefer to play chess, not 'fastest finger'. Some games end up being almost brainless arcade games when there's a dead draw but you have to get to 50-move or 3 x repetition to prove it against the clock, or mate with K+R vs K in 20 seconds.
Too many people on this site (erroneously) believe that increments give a greater opportunity for engine use.
Even when watching games between 2300+ players, they sometimes end up in silly, and blunder-ridden, time scrambles at Game in 3/0.
I always try to play with at least a 5 second bonus. That way you have a fighting chance to get to the end of the game ON THE BOARD, instead of the clock.
Regardless, there's no accounting for taste, or for some folk's reasoning.
Seven years later, I just realized that the difference between two GMs playing Games in 3/0 versus playing Games in 3/1 is about an extra 30 moves before the game reaches a conclusion on the clock. Instead of a win in 60-80 moves, their games at 3/1 speed will often go over a hundred moves. WOW, and lots of those extra moves are still excellent "killer moves" Ha!
Can people justify this way of playing?
Seems like for any really long game (lots of moves) it'll be just a race for time. Even a 2 second increment can at least mean you don't lose when you're two queens up.
Because it's more fun.
Some people play with increment, some people play with excrement.
All FIDE competitions are with increment: 90|30, 15|10, 5|3, 3|2.
Actually not all the time.
In my country, there are lots of no-increment rapid tournaments, four of which appeared last month (albeit it being the same tournament but having four different sessions) as FIDE rated 20 minutes per side with no increment.
Now that I think of it, I have only heard of 25-minute tournaments in my country but not 20-minute ones.
increments are for those who cant properly manage their game time.
Yep. Lots of excuses being made but I do not like playing with increments for this reason. If you don't want to risk losing on time, don't play blitz chess. If you have a winning position but you used 3 minutes to get it as opposed to your opponent's 2, then you should not be rewarded for taking more time to think in a BLITZ chess game.
increments are for those who cant properly manage their game time.
I don't like to manage my time when it's fixed while the length of the game is not. I don't know how to play 10 minute games with consistent quality when the number of moves can be anywhere between 20 and 100. Increments solve this problem - longer games get more time.
I can really only play correspondence chess without a clock. I am not very good and can't think fast enough. 
I admire those who can play with one though.
cause its fun but having increment definitely helps for a much more logical and less cheesy game
I've played it OTB with analogic clocks. Really funny, although I'm really bad at it.