\(B=\dfrac{1}{\sqrt{5}-2}+\dfrac{4}{3+\sqrt{5}}=\dfrac{\sqrt{5}+2}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}+\dfrac{4\left(3-\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\)
\(=\dfrac{\sqrt{5}+2}{5-4}+\dfrac{4\left(3-\sqrt{5}\right)}{9-5}=\sqrt{5}+2+3-\sqrt{5}\)
\(=5\)