Not sure there is really a shortcut...at least I don't see one immediately. You could factor out 5^12, giving you
(5^12)(1+5+25) = 31(5^12)
Then, I expressed 5^12 = 25^6 = 625^3.
From there I multiplied out 625*625*625 and multiplied the result by 31. This does take a minute or two to do by hand, so there may be an easier way, but I am not seeing it.
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