It's more than $5, but what you're looking for ("cloud" gaming PC without walled garden) exists. You can rent a VM with GPU, for example from Paperspace [1], and install a remote desktop app that optimizes for latency, for example Parsec [2].
In the past there was the french company Shadow [3] that offered gaming-ready Windows VMs, but they filed for bancruptcy in 2021, not sure about their current status.
Not affiliated with them, but I tried both (Shadow before their bancruptcy, Paperspace+Parsec maybe a year ago) and both worked okay. A bit too much latency for my taste so I stopped using it, but with better connection speed and lower distance to the data center it might be acceptable.
Personally gaming sounds so expensive considering you’re just burning time. Probably cheaper than clubbing or travelling tho.
The glory days of cloud gaming, for me, were when i was a beta subscriber to GeForce Now and I could play all my Steam and Blizzard Games at high graphics. Slowly the picking got slimmer and slimmer, and then Nvidia started charging.
My dream is to pay $5 a month to play my existing games on a decent computer without having to buy one. Given the heavyweights who have tried and failed to provide this, I’m guessing that it’s not going to happen any time soon, or at all. The more likely future is platform-specific, siloed.