$$10000 = \frac{3384}{100}x^5-\frac{5478}{10}x^4+\frac{33712}{10}x^3-\frac{90285}{10}x^2+\frac{10122}{1}x+\frac{4890}{100}$$
Answer
$$ \begin{matrix}x_1 = 5.06016 & x_2 = 0.4528+1.2636i & x_3 = 0.4528-1.2636i \\[1 em] x_4 = 5.11109+2.47613i & x_5 = 5.11109-2.47613i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 10000 &= \frac{3384}{100}x^5-\frac{5478}{10}x^4+\frac{33712}{10}x^3-\frac{90285}{10}x^2+\frac{10122}{1}x+\frac{4890}{100}&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot10000 &= 100 \cdot \frac{3384}{100}x^5-100\frac{5478}{10}x^4+100\frac{33712}{10}x^3-100\frac{90285}{10}x^2+100\frac{10122}{1}x+100\cdot\frac{4890}{100}&& \text{cancel out the denominators} \\[1 em]1000000 &= 3384x^5-54780x^4+337120x^3-902850x^2+1012200x+4890&& \text{move all terms to the left hand side } \\[1 em]1000000-3384x^5+54780x^4-337120x^3+902850x^2-1012200x-4890 &= 0&& \text{simplify left side} \\[1 em]-3384x^5+54780x^4-337120x^3+902850x^2-1012200x+995110 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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