#### Answer

$-32-26i$

#### Work Step by Step

Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ then
\begin{array}{l}\require{cancel}
(1-7i)(3-5i)
\\\\=
1(3)+1(-5i)-7i(3)-7i(-5i)
\\\\=
3-5i-21i+35i^2
.\end{array}
Using $i^2=-1$ and then combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
3-5i-21i+35i^2
\\\\=
3-5i-21i+35(-1)
\\\\=
3-5i-21i-35
\\\\=
(3-35)+(-5i-21i)
\\\\=
-32-26i
.\end{array}