No phones are capable of 5G yet (because Qualcom hasn't made 5G-capable modems yet), no carriers are running 5G yet, so you're not going to see it at all until the end of 2018, and there won't be any phones with it until 2019. (Read this article.) But remember, gigabit 5G to the phone isn't going to do you much good if the carriers are only receiving packets from the internet at 5mbps. It may reduce latency from the server to you (it will reduce latency from the carrier to you - but if there's 500ms latency from the server to the carrier, you'll see 500 ms latency from the server), it will definitely allow the carriers (except, maybe, T-Mobile) to pack more data into the same tower, but we're already getting close to 100mbps on 4G, so the proof of concept for that is done, and the internet itself is still nowhere near that unless you live near the server (or your carrier's entry point to the backbone is near the server, for cellphones).
Once your carrier is running 5G, and you buy a 5G-capable phone, you might see a faster speed from Ookla, but your downloads from a given, distant, server, or your game play from a distant server, probably won't change much.