Solving a double integration in parametric form

I need help to find the surface area of the part of the paraboloid that lies in the first octant, meaning $x,y,z\ge 0$, of $z=5-x^2-y^2$.

So I found that I need to parametrize the paraboloid using cylindrical coordinates: $${\bf x}(u,v) = (u \cos v, u \sin v, 5 – u^2),$$with $0 \leq u \leq \sqrt{5}$ and $0 \leq v \leq \pi/2$. Then compute: $$\int_0^{\pi/2} \int_0^\sqrt{5}\|{\bf x}_u \times {\bf x}_v\|\,{\rm d}u\,{\rm d}v.$$ But I need help doing this. Can someone please help me continue on with this?

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