Try giving your 2.4 and 5 GHz networks different SSID names. I'm not familiar with connecting the Dot, but if it gives you any choice of networks (I would hope it would) then you can specify the one you want. If both frequencies have the same SSID, I'm sure it will always choose the 5 GHz connection first.
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I'm not sure I accept Amazon's explanation. As long as both wireless devices are connected to the same overall network, I can't see how one being on 5 GHz while the other is on 2.4 GHz could matter. The Roku and Amazon aren't communicating directly with each other wirelessly, they are using the underlying network connection, which has nothing to do with the wireless frequencies in use. Unless there's a setting in your router that is separating the two frequencies into to separate sub-networks, sometimes labeled VLANs. Of if your router has a setting enabled that blocks one wireless devices from seeing another. Those exist as well, usually for privacy from guest connections.
Dan
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