$ (5^* times 5^*)_{asym}={10}$ in A. Zee's book p.409 versus PDG Sec.114

What is the mathematical or physical way to understand why the 4th and 5th components in the Georgi Galshow SU(5) model has the SU(2) doublet $(1,2,-1/2)$:
$$
begin{pmatrix}
nue
end{pmatrix}
$$
with left-handed $nu$ in the 4th component and $e$ in the 5th component of $5^*$;
while in the contrary,
the SU(2) doublet $(3,2,1/6)$:
$$
begin{pmatrix}
ud
end{pmatrix}
$$
with the left-handed $u$ in the 5th component (column or row) and $d$ in the 4th component (column or row) of $10$?

My question is that why not the left-handed $u$ in the 4th component (column or row in the anti-symmetrix rank-5 matrix, say in Zee’s book p.409 below) and $d$ in the 5th component (column or row in the anti-symmetrix rank-5 matrix, say in Zee’s book p.409 below) of $10$?

My understanding is doe to the complex conjugation
$$
(5 times 5)_{asym}={10}^*
$$
instead of
$$
(5^*
times 5^*
)_{asym}={10}.
$$
But is it this the case? Would $2^*$
flips the doublet component of 2?
$$
2: begin{pmatrix}
vv’
end{pmatrix}to
2^*
begin{pmatrix}
v’v
end{pmatrix}?
$$

In contrast, we see the PDG writes in a very different manner: https://pdg.lbl.gov/2018/mobile/reviews/pdf/rpp2018-rev-guts-m.pdf

Can we compare the two notations? Notice the contrary locations of $nu, e, u, d$.