$\text{a)}\sqrt[5]{-3}-\sqrt[5]{96}+2\sqrt[5]{729}=\sqrt[5]{-1\cdot 3}-\sqrt[5]{32\cdot 3}+2\sqrt[5]{243\cdot 3}=\sqrt[5]{-1}\cdot \sqrt[5]{3}-\sqrt[5]{32}\cdot \sqrt[5]{3}+2\cdot \sqrt[5]{243}\cdot \sqrt[5]{3}=-\sqrt[5]{3}-2\sqrt[5]{3}+2\cdot 3\cdot \sqrt[5]{3}=-3\sqrt[5]{3}+6\sqrt[5]{3}=3\sqrt[5]{3}$  

---

$\text{b)}\frac{\sqrt[4]{1250}-\sqrt[4]{162}}{\sqrt[4]{512}}=\frac{\sqrt[4]{625\cdot 2}-\sqrt[4]{81\cdot 2}}{\sqrt[4]{256\cdot 2}}=\frac{\sqrt[4]{625}\cdot \sqrt[4]{2}-\sqrt[4]{81}\cdot \sqrt[4]{2}}{\sqrt[4]{256}\cdot \sqrt[4]{2}}=\frac{5\sqrt[4]{2}-3\sqrt[4]{2}}{4\sqrt[4]{2}}=\frac{2\sqrt[4]{2}}{4\sqrt[4]{2}}=\frac{1}{2}$  

---

$\text{c)}\sqrt[13]{5^{39}}=\sqrt[13]{5^{3\cdot 13}}=\sqrt[13]{{\left(5^3\right)}^{13}}=5^3=125$  

---

$\text{d)}{\left(\sqrt[7]{\sqrt[3]{-125}}\right)}^7=\sqrt[3]{-125}=-5$