What forms do I fill out to properly record a like-kind (1031) exchange when we have lived in it as a primary residence for five+ years?

"What forms do I fill out to properly record a like-kind (1031) exchange"

The form would be Form 8824, but the property (both the relinquished and the replacement) must be that which is held for productive use in a trade or business or for investment; a primary residence would not qualify.

IRC §1031(a)(1)

Primary residence does not qualify.