I have ran a 25' snake down the drain but it didn't clear it. I have a vent pipe about 12" away from the drain pipe with the cleanout about 18" above the floor. Should I remove the cleanout and snake from there?

As fatmatrat said, yes, snake from the cleanout. There is a chance the snake vent up the vent, instead of down the drain when you snaked from the standpipe of the washer drain. Snaking from the cleanout will ensure the snake goes down the drain.