Probably not, but to be sure, find the transmission model number on both and compare. The transmission number is on a white tag, and is a series of letters and numbers. My 2003 is a BVGA. Your 2005 may be a PVGA? What is the Ridgeline?
Another way to check: go to car-part.com and do a search for a junkyard replacement. Only compatible parts will be listed, and the source vehicles will be detailed there. See if Ridgeline comes up as a donor vehicle in the search.