Can anyone Explain how The Federation works to me like I am five years old?

The Federation is a representative republic, with an elected president as the head of the entire interstellar state. An election is held every four years, and a president may serve for an unlimited number of terms.

Political and direct administrative power is held within the Federation Council, which is composed of one councillor from every Member World. There is no limit as to how many terms a person may serve as councillor. T'Latrek of Vulcan, for instance, served on the Federation Council for nearly a century. Each individual Member determines how its councillors will be determined; the First Minister of Bajor, for instance, nominates that world's councillor and the Chamber of Ministers ratifies him or her, while the electorates of many other Members elect their councillors directly.

The Federation government has several executive departments whose heads form the Presidential Cabinet, who advise the president on their issues of jurisdiction and run their departments on a day-to-day basis. Cabinet members can have strong influence on Federation policy based upon their work with the president and the appropriate members of the Federation Council.

By the late 23rd and 24th century, the capital city of the Federation is Paris, and the capital planet is Earth. The seat of government is the Palais de la Concorde.

Memory Beta article on The Federation

Five-year-olds must be pretty advanced in the 24th century.
- In 24th century Starfleet, calculus was taught to children around age ten or older. On the USS Enterprise-D, Harry Bernard hated calculus, despite the fact that his father told him everyone needed a basic understanding of it. (TNG: "When The Bough Breaks")
  Memory Alpha page on Calculus

A bunch of people set up public bulletin boards, and agree to copy whatever gets posted on one of them to all the others.

That is a very nice photo.

Thanks, whoever the home owner was did a great job with their landscaping! I was in awe.

The Wikipedia entry does a very good job in its first few paragraphs:

The fediverse (a portmanteau of "federation" and "universe") is an ensemble of social networks which can communicate with each other, while remaining independent platforms. Users on different social networks and websites can send and receive updates from others across the network.

ActivityPub, a W3C standard, is the most widely used protocol that powers the fediverse. Noted fediverse platforms include Mastodon, Lemmy, PeerTube, Pixelfed, and Threads.

I appreciate the information you shared about a standard. I was curious at how some level of control was implemented to advance The Federation without there being a sole source of power.

Possibly not for a five-year-old, but most people have an email account, and technically this is a federated network. Tuta, Proton, Posteo, and all the others are independent networks, but they can communicate with each other (unlike Facebook, Twitter, and others which require an account on each platform for communication).

Forum: People set up communities on their or someone else’s server. People have to individually find and register for each siloed community.

Aggregator site (i.e. reddit): Everyone sets up communities on the same server. A single account on the server can join and interact with any community they want, and aggregate them all together into a feed.

Federated aggregator (i.e. Lemmy): People set up communities on their or someone else’s server. They all use the same language so they can communicate with each other. You can make an account on any server and then visit any community, and aggregate them all together into a feed.