How much does the iPhone 5G cost in the US?

Online it says $199, but my friend said it's more expensive at the Apple Store. Details on the price (In the US), please?

Added (1). What exactly is a contract and what does it do? (I obv.know what a contract is, but what is the apple contract?)

Added (2). What is activation?

Depends on What Company You Buy It From, Apple In This Case Has The Cheapest One Starting At 300 Sprint As Them Starting From 199.00

It is $199 WITH A CONTRACT both online and in the Apple Store.

If you're not starting a contract, or eligible for an upgrade on your current contract, it costs $649.

If you have Verizon, you can get the iPhone 4 for free, or the 4S for $100. The iPhone 5 is around $200 but with activation and everything, it's almost $500

The iPhone5 varies IF you are eligible for an upgrade, the iPhone16gb is 199.99 32gb is 299.99 and 64 is 399.99. On Apple i'm pretty sure it is the exact same thing. Without a contract/buying in the middle of one it is somewhere between $700 and 800$.
The contract for cellphone companies (AT&T, Verizon Wireless, Sprint, and T-Mobile) is a contract that you have for a year or 2, and when you buy a phone you need to wait that long to get a new phone. It's the same exact for any phone you buy even apple.
If you mean activation by like activating your phone, it's something you need to do on your contract to be able to use the phone. If you don't have a contract and have maybe a pre-paid phone, wherever you buy it they would activate your phone for you.

Its called the iPhone 5 not 5G.

Yes the online price starts at $199 but those are on contract. Its not a contract with Apple, but rather with AT&T, Sprint & Verizon. What they entail depends on which carrier you go with.

Activation of course is getting the phone to start working as it is intended to.

Oh & when your friend said it was more expensive at the Apple Store, he/she was probably referring to the factory unlocked models which only Apple sells, but not as yet in the US.