There is a lamppost in my back yard. The light has not worked in the 5 years I've been in the house.

How do I check if there is any power to the lamppost, and how do I check what wire or circuit coming out of the house goes to that lamppost? I have a basic multitester.

Some yards away, I discovered the end of an electrical wire coming out of the ground. (maybe used to go to the lamppost) How do I check is that wire is live, and what circuit it is on?

I'm assuing I have to turn off power to the whole house first as I don't know what breaker the lamppost or the wire is on.

Thanks!

Check bulb, socket and fixture first.
2 sets of wire sticking out of the ground would be better. The one sticking out of the ground may be the end of a line.
See if you can find a switch at the front door that does nothing. See if there is a box on front of house, it may be a stop on the way to the post light.
An extension cord ran near light for a reference to see if neutral is intact, and to see if hot is present. One meter probe in extension cord hot, and other on post neutral to see if post neutral is intact. Do same to check for hot.

A wire locator( from 200- thousands of dollars will tell where it is buried and how deep.
I use a progressive(maybe between 200-300 dollars). It works in walls, underground, and through concrete. 3M and others also make locators.