It's averaged out over 5 seconds.
It's very easy to test:
Go into game and buy a meki pendant to start, then use mana.
It goes up steadily, and NEVER jumps up by 7 every 5 seconds.
gaming.stackexchange.com/users/23074/Masck
It's periodically.
If you have an item that generates gold per 10, such as Heart of Gold or Kage's Lucky Pick, then you get more gold over time, not a sudden burst every 10 seconds.
If you want to test this, then amass a large sum of money and go back to the base and buy a number of gold per 10 items and watch as your gold gain skyrockets.
This applies to all other stats such as Health or Mana Regen, or runes for Energy gain.
However, Force of Nature gives the 0.35% health every second on the dot.
Source: http://leagueoflegends.wikia.com/wiki/Health_regeneration
gaming.stackexchange.com/users/22276/Aceofgods
If you pay attention to the video, after 6 warmongs, Rumble ticks every second for Health Per 5 secs.
They're small amounts and though the video is fast, they are still per minute.
I don't know about gold or mana.
I assume they might be the same.
gaming.stackexchange.com/users/23228/lostpuppydog
I think this might help?
I don't know the video quality is a bit bad.
gaming.stackexchange.com/users/23131/FishyUrftheGreat
The actual healing effect from regeneration is applied every half-second, not every 5 seconds.
http://leagueoflegends.wikia.com/wiki/Health_regeneration
gaming.stackexchange.com/users/11969/Ryre
For health regen and mana regen items the effect is calculated every 0.5 secondsso for example if you have a total of 30 health regen.
every 0.5 seconds 3 health is added.
which over a 5 second period accumulates to 30 health.
Then there are items like the Rod of Ages which adds x amount of mana/health every 60 seconds.
but this effect is only applied once every 60 seconds and is not calculated or added per second As a general rule: hp/mp regen, gp/5 and damage over time is calculated per 0.5 seconds.anything else is added all at once like Rod of Ages.
Source:- myself (loads of buying regen/gp5 items / 2000 games of experience)-
http://leagueoflegends.wikia.com/wiki/Health_regen- http://leagueoflegends.wikia.com/wiki/Mana_regeneration
gaming.stackexchange.com/users/19798/Serge Bekenkamp
This mostly comes from the effects like HP regen and MP regen, is the amount spread over 5 secs or after 5 sec exactly?
If an item has the effect "XXX per 5 secs" is the effect over 5 secs or is it exactly on 5 secs?
gaming.stackexchange.com
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gaming.stackexchange.com/questions/60694
gaming.stackexchange.com/users/22120/Enix Blade ggClassic
It's periodically and averaged out over 5 seconds.  The effects apply over specific timings.
The community is explaining the mechanics behind the timing of effects.