I'm trying to apply the most simple math possible and it seems to add up.

After one second, their distance is √(5² + 1²) = ~5.1 ft

After two seconds, their distance is √(10² + 2²) = ~10.2 ft

After three seconds, it's √(15² + 3²) = ~15.3 ft

As speed is the rate of change of distance over time, you can see it's a constant 5.1 ft/s. You're free to point out any error, but I don't think you need anything more than Pythagoras' theorem.

The question specifically asks for their seperation speed at 5s to ignore any initial change in their speed as they first need to accelerate, I'd assume.