FindInstance with a Diophantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation

$$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes; I might be doing something wrong.

FindInstance[2012^2 == a^2 + b^2 + c^2 + d^2 + e^2 
    && a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]

But when I try

FindInstance[2012^1 == a^2 + b^2 + c^2 + d^2 + e^2 
    && a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]

I get an immediate result.

Answer

It does not seem surprising that a search space 2000 times larger results in a substantially longer computation time.

Here is a much more direct way to find a solution:

Sqrt @ IntegerPartitions[2012^2, {5}, Range[2012]^2, 1]

{{2011, 63, 7, 2, 1}}