Here is my current understanding of Bitcoin:
I have 10 bitcoins in my wallet.
If I send 5 bitcoins to someone else, I am sending the private key from my wallet to somebody’s public key address.
Those are combined into a new transaction that is later confirmed by miners. The miners confirm that I owned the bitcoins by checking my private key, and that the receiver’s public key is valid.
Then, the miners create a new private key that is sent to the receiver’s wallet.
On a simple True/False basis, is everything I have said right so far?
If so, what happens to the remaining 5 bitcoins in my wallet? Do they magically get a new private key, or what? How does my wallet know how many I have left, and how do the remaining bitcoins get a new identity?