#### Answer

$-\frac{7}{17}-\frac{23i}{17}$

#### Work Step by Step

Complex numbers are divided by multiplying the numerator and
denominator by the complex conjugate of the denominator:
Step 1: $\frac{3+5i}{-4+i}\times\frac{-4-i}{-4-i}$
Step 2: $\frac{(3+5i)(-4-i)}{(-4+i)(-4-i)}$
Step 3: $\frac{3(-4-i)+5i(-4-i)}{-4(-4-i)+i(-4-i)}$
Step 4: $\frac{-12-3i-20i-5i^{2}}{16+4i-4i-i^{2}}$
Step 5: $\frac{-12-23i-5i^{2}}{16-i^{2}}$
Step 6: $\frac{-12-23i-5(-1)}{16-(-1)}$
Step 7: $\frac{-12-23i+5}{16+1}$
Step 8: $\frac{-7-23i}{17}$
Step 9: $-\frac{7}{17}-\frac{23i}{17}$
The answer is in rectangular form.