We have a blue nest in a box in our garden with a camera Unfortunately yesterday a sparrow hawk took the female when she was out having a feed. There are 10 eggs in the box and she had been incubating for about 5 days. Should I clean out the box and hope

Such sad news about your Blue Tit but there's nothing to be done except to leave the nest as it is until end of breeding season when you can strip & clean the box for use either as a winter roost or a new nest next season!  It's always a great disappointment when things like this happen but is nature unfortunately!  

EDIT: Okay so apparently moving wild eggs, even if they’re orphaned, is illegal, so maybe don’t try my advice… But I would still call a local rescue to double check / ask for additional advice ‍♀️

Ten seems like so many potential bird lives to just leave to die…  Nature can be cruel… Maybe you could try asking a local wildlife rescue if they’d take the eggs? They have incubators & volunteers who look after orphaned baby birds, I don’t see why they wouldn’t do the same for fertilised eggs… Or if any bird farmers (ducks, chickens, turkeys) maybe have an incubator they could lend for them?? Couldn’t hurt to ask!

There are many reasons why you should not take presumably abandoned bird eggs from the wild to try to hatch not least because it is illegal ... a very informative article here ...

www.sialis.org/.../

Wow really? Even if you know they are orphaned and will die otherwise? And that they will be released to the wild once they fledge? Seems odd that we have laws in place to protect wildlife when the same laws are sometimes also accidentally detrimental to wildlife instead / as well… 

Also, that says it’s only illegal without a permit, surely someone at a wildlife rescue should have the appropriate permits to do so safely???

We are talking about unhatched eggs here which are in all probability already unviable ... it is a different story with orphaned or injured chicks who may stand a chance but then what?  No parents to be able to teach these poor unfortunates to survive in the wild! I can't imagine there would be many rescue organisations with the resources, staff & equipment to deal with raising multiple hatchlings nor the will to do so given what future lies ahead ... if every bird egg laid survives to adulthood the balance of nature would be severely affected ... let nature take care of it's own except in extreme circumstances!