For standard form I got $\displaystyle (x+4)^2=5$ but I should have got
$\displaystyle (x-4)^2=-5$ Mr F says: No, see below.
according to the vertex formula:
-b/2a
$\displaystyle y = a(x - h)^2 + k$ has a vertex at x = h. Your vertex formula told you that x = -8/2 = -4 therefore h = -4 which agrees with your earlier (correct) calculation.