Where to find the MTP mode in my Galaxy 5 phone and then how to transfer my photos from my phone to my MacBook Pro? Or at least have them automatically transfer from my phone to my drive in Google.
macOS by default does not support the MTP protocol. You'll need to download a utility provided by Google called Android File Transfer on your MacBook to transfer files from your phone to your laptop.
As for the second part, you can set up your photos to automatically be backed up to your Google Drive by going to Google Photos and selecting all the folders which you'd like to be backed up.