$\text{a)}{10}^{\log 17}={10}^{{\log }_{10}17}=17$     

$\text{b)}{5}^{1-{\log }_{5}3}=5^1:5^{{\log }_{5}3}=5:3=\frac{5}{3}$  

$\text{c)}{27}^{{\log }_{3}2}={\left(3^3\right)}^{{\log }_{3}2}=3^{3{\log }_{3}2}=3^{{\log }_3{2}^3}=3^{{\log }_{3}8}=8$  

$\text{d)}{2}^{1+{\log }_{4}5}=2^1\cdot 2^{{\log }_{4}5}=2\cdot 2^{{\log }_4{\sqrt{5}}^2}=2\cdot 2^{2{\log }_4\sqrt{5}}=2\cdot 4^{{\log }_4\sqrt{5}}=2\cdot \sqrt{5}$