If an item has the effect "XXX per 5 secs" is the effect over 5 secs or is it exactly on 5 secs?

This mostly comes from the effects like HP regen and MP regen, is the amount spread over 5 secs or after 5 sec exactly?

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.

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

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.

I think this might help? I don't know the video quality is a bit bad.

The actual healing effect from regeneration is applied every half-second, not every 5 seconds.

http://leagueoflegends.wikia.com/wiki/Health_regeneration