Answer
$$ (-3,2,3)$$
Work Step by Step
The parametric equations of the line are given by
$$ x=1-2t, \quad y=t, \quad z=1+t.$$
Now, substituting in the equation of the plane
$$ x-y+5z=10\Longrightarrow 1-2t-t+5+5t=10\\
\Longrightarrow 2t=4\Longrightarrow t=2.
$$
So the point of intersection is given by $$(1-2(2),2,1+2)=(-3,2,3).$$
