How can I split a 60 GB file into 5 GB pieces on a Mac?

I would imagine using a Disk Utility partition, but I didn't see the option in Disk Utility to split a larger partition into several.

How can it be done on a Mac?

I am doing this because I would like to Mail Drop the file.

OS X includes a command line tool called split. See man split for all the details.

You can call split using the Terminal.app and the command:

split -b 5000m MYBIGFILE

To combine it again, have the receiver store all parts in a dedicated folder, open Terminal there and run

cat x?? > MYBIGFILE

(This assumes that you used the default output names when running split.)