Rahisisha sehemu ya kwanza kwa kuondoa mzizi kwenye denominator.

Tunazidisha nambari na denominator kwa kiambishi cha $3-\sqrt{5}$, ambacho ni $3+\sqrt{5}$.

$$\frac{1}{3-\sqrt{5}} = \frac{1}{3-\sqrt{5}} \times \frac{3+\sqrt{5}}{3+\sqrt{5}} = \frac{3+\sqrt{5}}{3^2 - (\sqrt{5})^2} = \frac{3+\sqrt{5}}{9-5} = \frac{3+\sqrt{5}}{4}$$

Kutoka kwenye mlinganyo $-\frac{1}{4} + \frac{1}{4}\sqrt{5}$, tunaweza kuona kwamba:
$a = -\frac{1}{4}$
$b = \frac{1}{4}$
$c = 5$

Thamani za $a$, $b$, na $c$ ni:
$a = \boxed{-\frac{1}{4}}$
$b = \boxed{\frac{1}{4}}$
$c = \boxed{5}$