Question 355076
Let x = distance of the man from the base of the lamppost.
Then x + 5=distance of the tip of the man's shadow from the base of the lamppost.  Then by a direct application of similar triangles,
{{{(x + 5)/6 = 5/2}}}.
After cross-multiplication, {{{2(x+5) = 30}}}.
{{{x+5 = 15}}}
{{{x = 10}}}.
The man is 10 m away from the base of the lamppost.