Squaring both sides, we get:
[tex]5 + 7\sqrt{5} = (a + b\sqrt{5})^2[/tex]
Expanding the right-hand side, we get:
[tex]5 + 7\sqrt{5} = a^2 + 5b^2 + 2ab\sqrt{5}[/tex]
Equating the real and imaginary parts, we get:
[tex]\begin{cases}a^2 + 5b^2 = 5 \\ 2ab =
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