Emergency services were called to the scene near junction 24 at Huntworth just after 8.30am on Thursday.
The collision on the southbound carriageway involved a lorry and six cars.
The female driver of one car and the male passenger of another car were pronounced dead at the scene, a police spokesman said.
A woman from each of those vehicles was taken to Southmead Hospital in Bristol with serious injuries.
Two other victims of the crash, who are not believed to have life-threatening injuries, were taken to Musgrove Park Hospital.
Another person was treated at the scene and later released.
Pictures from the crash site showed emergency workers next to a badly crushed blue car.
Inspector Frazer Davey said: “I’d like to thank people for their patience while the emergency teams are working at the scene and as the vehicles are being recovered.”
“While I appreciate how disruptive the road closure is I’m sure people will understand our need to carry out a thorough investigation to establish exactly how this happened.”
The M5 was closed in both directions between junction 24 and junction 25 after the crash.
The northbound carriageway re-opened at around 12pm.
The southbound carriageway remains closed while emergency services carry out an examination of the scene and recover vehicles.