SG-5 was one of the original nine SG teams created by presidential order after Colonel Jack O'Neill's second expedition through the Stargate to Abydos. (SG1: "Children of the Gods")
This team were assigned to complete the mission on Aemonus, when SG-1 traveled back in time instead. Captain Patrick Ferguson sent a transmission at 1040 hours indicating that SG-1 never arrived on P2X555 and recommended a search and rescue operation pending approval. (SG1: "1969"), Showtime Stargate Command Code Name: "1969".
They were once visiting an abandoned Goa'uld palace and afterwards displaying signs of drug addiction after being expose to the Light Matrix Hologram, due to this condition Lt. Dean Barber committed suicide and a few days later the rest of his unit died. (SG1: "The Light")
A few years later, they are off-world when Teal'c was trapped in transit between Stargates. They are therefore transported back to Earth using the Russian Stargate. (SG1: "48 Hours")
The Military unit was led by Major Harper. They along with SG-3 provided backup for SG-1 on the planet P3X-439. (SG1: "Lost City, Part 1")
SG-5, led by Major Altman, later accompanied Lt. Colonel Samantha Carter on off-world mission to investigate possible Supergate building site. (SG1: "Prototype")
SG-5, along with SG-4, was sent as back-up in the failed attempt to dial the nine chevron address on Langara's Stargate to send reinforcements to Destiny. (SGU: "Seizure")
Behind the scenes
In "Seizure", Richard Woolsey mistakenly refers to the two teams as "SG-1 teams 4 and 5".