Can I charge someone for a hand gesture such as a high five or a handshake? How would a receipt be written for such a thing? It seems like a silly question but I am genuinely curious and want to make sure my social experiment isn't subject to any sort of weird laws that I don't know about.
The way law works is that you don't need to find a law which says you can do something. Instead, there needs to be an absence of a law which says you cannot do that thing. In other words, you can do anything you want so long as there isn't a law which says you can't. It's unlikely that you will find a law in any jurisdiction which says you cannot charge for a handshake.
If you want the charge to be legally binding on the other party, then you need to ensure that the formalities of a valid contract are met. In particular, either each side needs to provide consideration (something of value) or the contract needs to be executed as a deed (england-and-wales).
The party who pays the charge is clearly providing consideration. What about the handshake? Is it something of value?
The rule is that consideration must be "sufficient" but does not need to be "adequate". That means that it must have some value (however small) but it doesn't need to be valuable enough to be a fair bargain for the parties. This was confirmed by the House of Lords in Chappell & Co. v Nestle Co. Ltd (1960) AC 97 (england-and-wales) which held that empty chocolate wrappers, which would be thrown away upon receipt, were sufficient consideration. A more common example of low-value but sufficient consideration is a "peppercorn" which is often used as token consideration where (in practical terms) a party is not offering anything of substance.
Note that "value" doesn't need to mean something that benefits the recipient. It can also be something which detriments the person who provides it. The courts have held that a promise to do something you were not otherwise legally required to do is sufficient consideration. For example, in Hamer v Sidway (1891) 27 NE 256 (new-york-state), the court held that a promise to quit smoking was sufficient consideration.
It doesn't matter whether the recipient values the consideration or not. In Chappell (see above) the court held:
It is said that when received the wrappers are of no value to Nestle’s. This I would have thought irrelevant. A contracting party can stipulate for what consideration he chooses. A peppercorn does not cease to be good consideration if it is established that the promisee does not like pepper and will throw away the corn.
A handshake is almost certainly sufficient consideration because it involves doing something that you were under no legal obligation to do before you agreed the contract.
How you write a receipt is a matter of personal choice and therefore off-topic.
Can I charge someone for a hand gesture such as a high five or a handshake?
Only if you and the counterparty agree beforehand on the topic of compensation. That is because the formation of a contract requires that the parties commit to the terms and conditions knowingly and willfully. Since typically nobody charges for a hand gesture, you need something to supersede the common presumption that also your handshake or high five is for free.
Obviating the agreement about compensation is likely to render a controversy undecidable. For instance, once the handshake is completed and you tell the counterparty to pay you $5, the counterparty could say "Quite the contrary, you owe me $10 for the handshake with me".