The five people were killed in two separate incidents and authorities say the suspect is still at large.
The shootings took place in Ascension and Livingston parishes, about 70 miles west of New Orleans.
On Facebook, the Ascension Parish sheriff's office said two people were shot dead in the city of Gonzalez with the victims identified as a husband and wife Elizabeth and Keith Theriot, both 50.
Their 21-year-old son, Dakota Theriot, is being sought by authorities on first-degree murder charges, illegal use of weapons and home invasion.
Livingston sheriff Jason Ard confirmed on Facebook that the three deaths happened in his parish on Saturday.
The victims were named as Billy Ernest, 43, Tanner Ernest, 17, and Summer Ernest, 20.
Authorities believe the shootings in the two parishes are connected.
Investigators from both jurisdictions are working together.
The authorities believe the suspect shooter is driving a 2004 Dodge Pick Up, which was grey on top and silver on the bottom.
Both sheriffs offices urge anyone with information to contact them immediately.
