We have to start with a number [tex]x[/tex], compute [tex]f(x)[/tex], and then use this result as input for [tex]g(x)[/tex]
When you give [tex]x[/tex] as input to [tex]f[/tex], it returns [tex]-x^2-1[/tex]:
[tex]x\mapsto f(x)-x^2-1[/tex]
Now, [tex]g(x)=x+5[/tex] simply means that [tex]g[/tex] will return its input plus five.
In this case, the input is [tex]f(x)[/tex], so we have
[tex]g(f(x))=f(x)+5 = -x^2-1+5=-x^2+4[/tex]
