How does a transaction get into the Mempool

I'm trying to understand how nodes work. If I send a transaction that says to send $5 to XYZ, but I don't have $5 or the transaction fees to do so, does the original node processing the request filter out this request?

I'm wondering how this works. If someone was to send me $20 but the transaction is sitting in the mempool, would I be able to get my $5 transaction into the mempool while the other transaction is waiting to be processed? Or would I need to wait for the $20 transaction to actually be mined first before I would be able to get my $5 transaction into the mempool.