Let $x_1, x_2, y_1, y_2$ be real numbers satisfying the equations:
1. $x_1^2 + 5x_2^2 = 10$
2. $x_2y_1 - x_1y_2 = 5$
3. $x_1y_1 + 5x_2y_2 = \sqrt{105}$

Find the value of $y_1^2 + 5y_2^2$.

Let's think step by step and output the final answer within \boxed{}.
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