Question 715744
It's {{{highlight(x=5)}}} .
If a parabola has the equation {{{y=ax^2+bx+c}}} 
the equation of its axis of symmetry is {{{x=-b/2a}}}
In your case {{{a=-1}}} and {{{b=10}}}, so {{{-b/2a=-10/2/(-1)=5}}}
 
However, you do not need to remember formulas if you realize that you can transform the equation {{{ y= -x^2+10x+3 }}} into
{{{y=-(x-5)^2+something}}}
{{{-(x-5)^2=-(x^2-10x+25)=-x^2+10x-25}}} so adding {{{28}}} to both sides of
{{{-(x-5)^2=-x^2+10x-25}}} we get
{{{-(x-5)^2+28=-x^2+10x+3}}}
which tells you that {{{y=-(x-5)^2+28}}} is another form of the equation of your parabola,
and this form tells you that the maximum height is 28, reached at time 5.