I just bought an equinox 2005 LS and I dont know how to lock the rear door.

To unlock the liftgate, press the unlock button on the Remote Keyless Entry (RKE) transmitter twice or use the power door lock switch.
To lock the liftgate, press the lock button on the RKE transmitter or use the power door lock switch. The liftgate does not have a key lock cylinder.
To open the liftgate, pull up on the handle located in the center of the liftgate.
When closing the liftgate, use the molded handles to pull the liftgate down. Push the liftgate closed until it latches.