Deathbringer Regent is a dragon that reads
When Deathbringer Regent enters the battlefield, if you cast it from your hand and there are five or more other creatures on the battlefield, destroy all other creatures.
And Phantasmal Image:
You may have ~ enter the battlefield as a copy of any creature on the battlefield, except it’s an Illusion in addition to its other types and it gains “When this creature becomes the target of a spell or ability, sacrifice it.
My question is if I play Phantasmal Image copying a Deathbringer Regent, it does copy the ETB but does it also count as "cast from your hand" and destroy all other creatures if there are 5 or more other creatures?