Even with a very directive antenna (or its black magic alternative, beam forming) it would use up a lot of spectrum over those 5 miles to deliver that 0.3kbps, worsening the connectivity of many people all around you. You'd hate it if everyone else was also doing it near you. Battery life would suck too.
Better connect to something else nearer to you, making a fairer use of the available radio spectrum, or if you absolutely need to connect to your own equipment, switch to a protocol more suited for such needs, like LoRa or even a custom-purpose version of Wi-Fi called HaLow (aka .11ah: https://en.wikipedia.org/wiki/IEEE_802.11ah)
Very roughly, every doubling of distance reduces received power and therefore theoretical data rate by a factor of 4. At 20 yards, I can get 2 Gbps out of my wifi, so at 5 miles, I can get 8 kbps with the same transmit power and antennas. Still plenty for instant messaging.
Better connect to something else nearer to you, making a fairer use of the available radio spectrum, or if you absolutely need to connect to your own equipment, switch to a protocol more suited for such needs, like LoRa or even a custom-purpose version of Wi-Fi called HaLow (aka .11ah: https://en.wikipedia.org/wiki/IEEE_802.11ah)