Answer
The limit is
$$\lim_{(x,y)\to(a,b)}\frac{5f(x,y)}{g(x,y)}=\frac{20}{3}.$$
Work Step by Step
It is given that
$$\lim_{(x,y)\to(a,b)}f(x,y)=4,\quad \lim_{(x,y)\to(a,b)}g(x,y)=3.$$
First, we will use the rule the multiplying constant (in this case $5$) can be put in front of the limit, and then the rule that the limit of the quotient is quotient of the limits:
$$\lim_{(x,y)\to(a,b)}\frac{5f(x,y)}{g(x,y)} = 5\lim_{(x,y)\to(a,b)}\frac{f(x,y)}{g(x,y)} = 5\frac{\lim_{(x,y)\to(a,b)}f(x,y)}{\lim_{(x,y)\to(a,b)}g(x,y)}=\\
5\times\frac{4}{3}=\frac{20}{3}.$$
