5KHz is pretty low, it would be difficult finding anything in the ham category because no ham bands are that low. You would need to probably build your own receiver. The good news is that 5KHz is super low frequency and could easily be received with a crystal detector. Antenna connects to an LC resonator centered at 5.3KHz, pass the result of this through a diode and then into a microcontroller. Many have analog input pins and analog comparators built-in that can trigger an interrupt. You would need to figure out what voltage level you expect to see from the detector when a heart beat signal is sent and then apply that voltage to the other side of the comparator. Some microcontrollers even have a real analog voltage output that could allow you to adjust the voltage through software. The microcontroller would then trigger an interrupt and do something every time a heart beat signal is received (send it through serial to a PC, compute heart rate, display something on a LED screen, etc).
If you need to broadcast at 5.3KHz, that's pretty easy too. There are numerous designs out there for a basic CW transmitter (https://makerf.com/posts/ten-minute-transmitter). You may have trouble finding a crystal centered at your 5.3KHz frequency.
If you need to broadcast at 5.3KHz, that's pretty easy too. There are numerous designs out there for a basic CW transmitter (https://makerf.com/posts/ten-minute-transmitter). You may have trouble finding a crystal centered at your 5.3KHz frequency.