Arnold Schwarzenegger and The Mentalist connection
Arnold Schwarzenegger was the governor of California when the Mentalist first aired. As the California Bureau of Investigation is the highest crime fighting and enforcement department of the Californian executive branch, they would typically have a portrait of the Californian Governor in their office.
That portrait is remarkably close to the real life official photo portrait of Governor Schwarzenegger. The only change would be the cloud like background instead of a flat blue. Note that the photographic portrait has been officially replaced by the painted portrait unveiled in 2014, as is tradition for Californian Governor portraits. (As far as I can find. The cache for the Californian Governor history website for Schwarzenegger only goes to 2010, and the portrait may have been updated on each of his three election wins/terms).
Official circa 2010 vs your Screenshot:
It gets muddied as Arnold left office in Jan 2011, while Season 5 premiered in September 2013. Two years after a new Governor was elected. Of course, the show, like many, has no fixed time setting, nothing to explicitly say it is set in real time. So season 5 could be set in 2010 while it aired 2013. Season 6 introduced a 2 year time skip, again without explicitly detailing a fixed date.
It could also be that the portrait just wasn't updated (in or out of universe), or that the CBI had a policy of having portraits of multiple former and current governors. But without more info that's just speculation.
Update: As OP has clarified, the episode takes place in a flashback. The show started in 2006, and Schwarzenegger was governor starting in 2003. This gives a wide date range in where the portrait would be a valid representation of the then current governor and executive branch leader of the State of California.