Here, I understood that the transaction size depends on the amount of wallet addresses, which are part of the transaction (sending 5$ to one and 5$ to second wallet?)
It does not depend on the number of addresses, but the number of outputs. It does not matter if you are spending five outputs across five addresses or five outputs all on the same address - the transaction size, and therefore the necessary fee, will be identical.
As per my
analogy earlier in this thread with physical cash, it does not matter if you take five physical coins out of your pocket, or if you take five physical coins from five different people. If you put these five coins in an envelope and send them through the mail, the price you pay for postage will be the same.
So if I assume, that if I split the amount on two receiving wallets, the transaction sizes increases and the whole transaction will be more expensive.
I've explained the size structure in
this post. 1 inputs and 2 outputs will be 140 vbytes for a segwit transaction. Each additional input adds 68 vbytes, and each additional output adds 31 vbytes.