Backyard drain is backed up- any ideas?

Our backyard drain on the ground, which also connects with the downspout from roof, backs up and water eventually makes its way into the basement. I tried filling it with the hose and after about 10 seconds it backs up with water. It does eventually go down after a long while and very slowly. I tried a 5′ toilet snake with no luck. What’s the best way to get it fixed? Is this an easy enough fix by renting a more industrial snake or is there more know-how involved that makes it worthwhile to get a company in to do it? If it matters, I think the clog is maybe just 10 feet or so down the drain, judging by how much hose water it takes to back it up and the fact that it backs up pretty quickly. Any ideas welcome and/or recommendations for companies who you’ve used to fix this issue.