Well no – they won’t pay out £5k on a bike worth £5.6k. They will tell you it is uninsured because the value was more than £5k
yes, normally if you under-insure (deliberately or accidentally) and you have a loss, the insurer will apply condition of average to give a pay out relative to the insured value you have actually been paying the premiums for (calculated as sum insured / actual value of the item x value of the loss). this is to ensure your premium contribution to the pool of risk is fair & equitable
however i’m not sure in this case it would count as under-insurance as it is the insurer that is limiting the value that you can insure ie not letting you insure full value by having a 5k limit.
i would speak to them and see what they say, but i suspect you might be ok as they have set a limit of indemnity of 5K and you are paying premium proportionate to that, so in the event of a total loss (ie your bike getting nicked) your premium contribution has been fair & equitable (ie you’ve not been underpaying). average might get applied in the case of a partial loss (ie damage to the bike) but as theft is the big issue that shouldn’t come into play.
even if average was applied you should still get a pay out of c £4,400 which while not the full amount, is not disastrous
of course i could be completely wrong as it’s been a while since i did my claims practice exams