What happens if you go back in time through a time machine while carrying another time machine's core?

Say you have 2 time machines and you activate both at once.

After 5 years, you take TimeMachine-A's core with you and go 5 years back in time through TimeMachine-B, to the point in time where both were activated.

Then immediately after, you use TM-A to go 5 years back in time again.