Is this correct?
y^2/25 + x^2/21 =1
Vertices: (5,0),(-5,0)
Foci: (0,2),(0,-2)
Since 25 > 21, the ellipse is long on the y-axis. So, the vertices are (0,5) and (0,-5)
You should have immediately seen your answers were incompatible. The foci must lie on the major axis.
Your foci are correct.