There are some chest transmitters that work on 5 kHz, but maybe it's worth just buying a more modern one (maybe also Bluetooth ones exist nowadays - I've not checked).
I have a 5 kHz one somewhere, and out of curiosity I once tried to receive the signal with it. I can't recall all the detail, I think the 'packet' is something like three small pips of 5 kHz, and you need to measure the distance between a couple of them. I'm sure you'll find the documentation online by googling. I don't have a circuit, I merely experimented until I could see something on the 'scope. I used a coil wound on a loo roll cardboard tube (Edit: actually now I think more, it was a piece of a poster tube, so probably approx 3 inch diameter), and some capacitor across it to act as the resonant circuit. Then, I simply used a few op-amp stages, some with filters. I think I also experimented with a switched capacitor filter but it wasn't necessary. That was all sufficient to see a clear signal from half a meter away or so (enough distance to reach a running machine etc), but I didn't decode with a microcontroller. Note that the frequency from the transmitter isn't precisely 5 kHz by the way (I think mine was off by two or three hundred Hz), so you might not want to filter too sharply.
Edit 2: If you want it to work over several meters I think you'd be better off using different type of chest strap, e.g. BLE if it exists, since then there are hundreds of off-the-shelf chips/microcontrollers, very decent range, and it's more sophisticated, won't interfere with other chest straps.