These are similar deep discharge batteries that Sinclair used on the Zeta bike motors, they were the 7Ah sized ones and only gave about 2 miles range, so going on that these might only give you about 6 or so miles range, (about 10 km).
But the C5 is much heavier than a bike, so your range may be less.
I use an 85 Ah leisure battery and get about 17 miles range on a full charge (27 km).
Charging the battery with a 10W Solar panel should be possible if you connect up directly to the battery using a 1A blocking diode to stop any surges from the circuit when switching on the motor damaging the Solar cell. It'll take a while to charge up the battery though, 24Ah would take 40 hours in full sunlight for a full charge with your 10W cell.
Cheers John