The equation of the line which has equal intercepts on the co-ordinate axes and passing through $\left(2,5\right)$  is

$\left(x,y\right)=\left(2,5\right)$

The line intercept form is $\frac{x}{a}+\frac{y}{b}=1$

$\frac{x}{a}+\frac{y}{a}=1$

$x+y=a$

It is passing through $\left(2,5\right)$

$\Rightarrow$ $2+5=a$

$a=7$

$\therefore$  the required line equation is $x+y=7$