Cryptography puzzle found on a website. Solutions to$a^2 + b^2 + c^2 + d^2 + e^2 = 2011^{2019} $

Question

There are 5 numbers a, b, c, d, and e. 1. How can you calculate the number of combinations that verify the following expression:

The form of the combinations : (a, b, c, d, e);

$a^2 + b^2 + c^2 + d^2 + e^2 = 2011^{2019} $

Is there a possibility where all the numbers are odd?

In the question they were referring to these five numbers as tuples.

Thanks for your time!