Why can't I call out - Panasonic KX-TG5632 Phone

It is possible the handset unit is not talking to the base station.

Try to receive an external call (made from other phone or cell) on the hands free and check if that works. If not then register the handsets to the base station.

It is also possible the phone has not been configured for the correct dialing protocol. Refer user manual at this site.

http://service.us.panasonic.com/OPERMANPDF/KXTG5631S.pdf