It goes against the grain for me to say this, given that my day job is working for the railways, but if it was me and my OH with five large bags between us then we wouldn't be thinking about doing LHR - LGW by train. It's perfectly possible - all the stations involved are fully accessible with lifts so that you don't have to tackle escalators or stairs. But boarding at Heathrow, changing trains at Farringdon from the Elizabeth Line to Thameslink and getting out of the station at Gatwick will each be a slow, laborious process!

Most of the buses between LHR and LGW are operated by National Express (NX) - this is, on paper, a much lower-stress option but, as you have noted, involves the wild card of the M25. If you do go down this route, bear in mind that NX's baggage allowance is one suitcase (max 20 kg) and one small bag per person. Extra suitcases are chargeable at GBP 10.00 in advance or GBP 15.00 on the day. A flexible Heathrow - Gatwick ticket usually comes in at around GBP 30.00 on NX, so for two of you plus three extra bags you would be looking at around GBP 90.00 - I don't know what a private van would cost but I suspect the premium over this might be small and well worth paying.

Neither option is risk-free - the M25 could be choked with traffic, or there could be a problem with the trains, both of which could delay you. However five hours seems like a pretty robust connection time so I wouldn't be hugely concerned whatever you do. Good luck!