Find the roots of $4 x^{2}+3 x+5=0$ by the method of completing the square.

(NONE) Given the quadratic equation: $4 x^{2}+3 x+5=0$.
To solve by completing the square,we first divide the entire equation by $4$:
$x^{2} + \frac{3}{4}x + \frac{5}{4} = 0$.
Now,we rewrite the expression by completing the square:
$(x + \frac{3}{8})^{2} - (\frac{3}{8})^{2} + \frac{5}{4} = 0$.
$(x + \frac{3}{8})^{2} - \frac{9}{64} + \frac{80}{64} = 0$.
$(x + \frac{3}{8})^{2} + \frac{71}{64} = 0$.
$(x + \frac{3}{8})^{2} = -\frac{71}{64}$.
Since the square of any real number cannot be negative,there is no real value of $x$ that satisfies this equation.
Therefore,the equation $4 x^{2}+3 x+5=0$ has no real roots.