SOmeone might have a 5000 ohm headphone.
This is a line amplifier, not a power amplifier. Well, a PA system mixer really. That output tube is a 6SN7, and that isn;t going to power much speaker.
The output transformer allows you to match the output to a wide range of impedances, from 10k ohms (5000-0-5000), down to 125 ohms. You can drive a balanced line or a single ended line.