The coordinates of the point where the line through $\left(3,-4,-5\right)$ and $\left(2,-3,1\right)$ crosses the plane $2x+y+z=7$ is

Equation of line through (3,-4,-5) and (2,-3,1) is $\frac{x-3}{-1}=\frac{y+4}{1}=\frac{z+5}{6}$=t

point (3-t,-4+t,-5+6t) subtute in given plane

 now solve this line and the given plane