Can I replace a Shimano Dura Ace 7800 10 speed cassette w/ a 105 5800 11 speed cassette?

This maybe a bit of a silly question but I've just put some old Bontrager Aeolus 5.0 on my aero bike (it has standard shallow shimano wheels at the moment) and they look amazing!
One problem is that the rear wheel has an old 10 speed Dura Ace (7800) cassette on it and I currently run 105 5800 11 speed. Is there any way of making my 11 speed cassette fit on the old wheels or do I have to save my pennies for the future?
Cheers in advance
One problem is that the rear wheel has an old 10 speed Dura Ace (7800) cassette on it and I currently run 105 5800 11 speed. Is there any way of making my 11 speed cassette fit on the old wheels or do I have to save my pennies for the future?
Cheers in advance
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Edit: whoops, didn't read the dishing bit.