Answer
$\frac{11}{25}-\frac{23}{25}i$
Work Step by Step
$\displaystyle \frac{5-i}{3+4i}=\frac{5-i}{3+4i}*\frac{3-4i}{3-4i}=\frac{15-20i-3i+4i^{2}}{9-16i^{2}}=\frac{15-23i+4*-1}{9-16*-1}=\frac{15-4-23i}{9+16}=\frac{11-23i}{25}=\frac{11}{25}-\frac{23}{25}i$