I don't have a Ridgeline, but I think you would be pushing it. I am sure someone will come along to tell you the same thing. I recently asked questions about a new van we were looking at and a hybrid I wanted to buy to tow. I was told that, even though it is below my tow capacity, it would be cutting it too close. We went ahead and got the van, but got a smaller hybrid.
Does the Ridgeline have the tranny and oil cooler? I wouldn't tow w/o it. If you find my original question about our new van, I think it is "found a new van?", not sure, then you will see the formula they gave me for determining how much I should actually tow. Notice I said "should". I think that I was told that 80% of my tow capacity is what I should tow. You have to take into account the gear and people you will be putting into the truck. 80% of 5000 is 4000. If it is only you and one or two other people in the truck and you are light packers, maybe, but you may have trouble on hills.
Of course, I am still a newbie, so I am just spitting back out information that I have been told.