$\text{a)}\left(a+5\right)\left(b+1\right)=a\left(b+1\right)+5\left(b+1\right)=ab+a+5b+5$  

$\text{b)}\left(x+2\right)\left(y-3\right)=x\left(y-3\right)+2\left(y-3\right)=xy-3x+2y-6$   

$\text{c)}\left(m-3\right)\left(n+7\right)=m\left(n+7\right)-3\left(n-7\right)=mn+7m-3n-21$   

$\text{d)}\left(p-4\right)\left(q-5\right)=p\left(q-5\right)-4\left(q-5\right)=pq-5p-4q+20$