Firefighters cut the occupants free after the crash in Flaxton Gardens at 3am.
Yorkshire Ambulance Service sent four ambulances to the scene, as well as three hazardous area response teams and two rapid response vehicles.
In total they had five patients, including one who had fractured their left leg and was suffering back pain, while another had a fractured wrist, and back and chest pain.
A third had a laceration to the knee and a fourth was suffering backpain.
A fifth person was discharged at the scene.
The occupant of the house had to go into alternative accomodation after a structural engineer from Leeds City Council checked the property.
Two crews from West Yorkshire Fire and Rescue attended from Hunslet.