There are different formats.
Standard: Cards that are usually 1-2 years old or less only. This year, that includes cards that have a "D", "E", or "F" regulation mark on the bottom left. See this article
for more on the current standard (which will go until end of 2022).
Expanded: Cards from Black and White or newer. 2011 or newer. This does include some banned cards
, fyi. Standard rarely bans, but Expanded always has a good amount.
Unlimited: no restrictions.
Plus other custom formats like GLC that have their own rules.
Standard is what should be default for competitive play unless you hear otherwise or agree otherwise. But for "at home" play, if you're not playing with anyone outside of home, make up whatever format you want - the only reason for the formats is to control what cards are available in what combination to keep play at a certain level [and to make more money, of course], so at home you can do whatever you're comfortable with. A five year old can certainly play DCE with no issues in my book. Just know that once he gets to the age where he wants to go to the local gaming store and play in paid tournaments or league play, he might need to change things (and if that's at 7 or 8 the format will be mostly changed anyway).
Check out Justin Basil's guide to rotation
if you want more specifics about standard format and rotations.
Also worth noting - while DCE is not standard, DTE (Double Turbo Energy) is still standard (same, but -20 attack damage) if he does want to play in a Standard event.