Electronic – Max length of extension cord for a 5kW load on 240

There is no single safe answer. It has a lot to do with the length of the cable, surrounding electrical noise, and how fast you want to go. Ethernet uses CAT5 cable to transmit at 10 Mbit/s for the slowest variety, so 1 Mbit/s is easily doable if you take the proper precautions. Note that with ethernet each signal gets its own twisted pair, and each pair is carefully terminated at the characteristic impedance of the cable at each end. Each pair is driven differentially and interpreted differentially, and is also designed so that it can't cause ground loops.

If you do all these thing, you can transmit 1 Mbit/s data on CAT5 cable for long distances, like 1000 meters. As you do less of these things, the usable distance will go down. If it's just board to board in the same chassis, for example, then you probably don't need to do much special. If you're going outside the unit, then differential line drivers and receivers could be useful.

Try something in your setup and look at the signals at the receiving end to get some idea of the noise margin, adjust as needed. Maybe use a protocol that can detect and recover from errors, and keep track of how often that is happening. There are too many ways to list here without more information.

Capacitance in the cable begins to affect serial communications, typically many manufacturers/devices set a limit of approximatly 15m or 50ft on cable lengths for anything up to 9600 baud, and about 4m for 38.4k. That being said, with decent cable it is easily possible to go longer in tested or non-commercial use, but I would stick to the guidelines for a commercial product, if only to leave an out for support calls.

If you really need length, RS232 to RS422/485 converters are very inexpensive, and you can run the differential modes (422/485) over two wires for well over 100m.

In your case, 5m really shouldn't be a problem at 38.4, as long as your cable is of reasonably quality. Almost any shielded multi-conductor cable should work at that distance, and probably three times it.