The equation of a line having intercepts $a,b$  on the axes such that $a+b=5,ab=6$  is

${\left(a-b\right)}^2={\left(a+b\right)}^2-4ab\Rightarrow {\left(a-b\right)}^2={\left(5\right)}^2-4\times 6\Rightarrow a-b=1$

By simplifying $a+b=5$ ,$a-b=1$   $a=3,b=2$

Equation of the line is $\frac{x}{3}+\frac{y}{2}=1\Rightarrow 2x+3y-6=0$  (when $a$  is x-intercept, $b$  is y-intercept)

$\frac{x}{2}+\frac{y}{3}=1\Rightarrow 3x+2y-6=0$     (when$a$ is y-intercept, $b$  is x-intercept)