Tyrese Gibson 's dogs don't have a care in the world ... running around a backyard and sitting for treats just a few weeks after they allegedly killed another dog.

TMZ has obtained photos and video of the five dogs at Tyrese's friend's house, taken Friday in Georgia. Fulton County Sheriff's Office

The video shows the dogs in a neighborhood backyard -- all look like Cane Corsos -- as they run around ... sitting down in the grass in an effort to get treats from the guys who are watching them.

The men then seem to take the dogs to the front yard ... letting them roam around -- in the yard and definitely not on the street. It shows a lot of trust with these animals who just a couple weeks ago killed a Cavalier King Charles Spaniel. Gallery Launch Gallery Getty

BTW ... our Tyres

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