Mr. Brown, who is serving the final 12 months of his second stint as governor, has granted 1,115 pardons and 51 commutations since taking office in 2011, Evan Westrup, the governor's press secretary said on Saturday.
Friday's executive actions weren't the first time Brown has pardoned immigrants facing deportation.
Trump's tweet, sent while the president was travelling from his Mar-a-Lago estate to the nearby Trump International Golf Club, may have been prompted by a report Saturday during the 6am hour of Fox and Friends, which Trump watches regularly. Sokha Chhan and Phann Pheach are the ones facing deportation to Cambodia.
Brown's pardons do not automatically stop deportation proceedings, but they eliminate the convictions on which authorities based their deportation.
But The Sacramento Bee reported that the five pardoned convicts included one convicted for spousal abuse, another for kidnapping, robbery and using a firearm, another for vehicle theft and two for possession of a controlled substance for sale.
Arpaio - the self-proclaimed "toughest sheriff in America" - is known for cracking down on undocumented immigrants and investigating unfounded claims questioning former President Barack Obama's citizenship.
Trump's Twitter attack on Brown is the latest in a longstanding feud between his administration and California over immigration.
California passed a law last October that, among other things, prohibits local law enforcement from asking individuals about their legal status. Chhan had served about a year in prison on a 2002 misdemeanor domestic violence conviction.
Pheach was convicted of possessing drugs and obstructing a police officer in 2005 and served six months in jail. Mena served three years of probation after being convicted of possessing illegal drugs in 2003. He now works at the nonprofit Ecology Center in Berkeley and assists at-risk youth.
"Daniel's case is of a person who made one mistake as a young adult, served his time and then completely turned his life around", the center said. He served five years in prison and three years on parole.