= Solution
The trigonometric <parallax> gives $d=1/0.02=50\,\mathrm{pc}$. Neglecting extinction, the <distance modulus> and given <bolometric correction> give
$$
M_V=5.3-5\log_{10}(50/10)=1.80515,\qquad M_{\rm bol}=M_V-0.1=1.70515.
$$
Using the specified solar bolometric magnitude,
$$
\boxed{\frac L{L_\odot}=10^{0.4(4.6-1.70515)}\simeq14.39,\qquad
\frac M{M_\odot}\simeq(14.39)^{1/3}\simeq2.43.}
$$
The mass estimate uses the cubic scaling normalized to solar values. A lifetime estimate additionally needs the fraction of fuel accessible to core burning. Take a core-accessible fraction $f_c=0.1$ and initial hydrogen mass fraction $X=0.7$. The supplied fusion energy gives
$$
q_H=\frac{26.7\,\mathrm{MeV}}{4m_p}\simeq6.4\times10^{14}\,\mathrm{J\,kg^{-1}},\qquad
\boxed{t_{\rm age}\sim\frac{f_cXMq_H}{L}\simeq1.25\times10^9\,\mathrm{yr}.}
$$
The alternative common solar-lifetime normalization $t\simeq10^{10}(M/M_\odot)/(L/L_\odot)$ years gives $1.69\times10^9$ years. Thus this simplified turnoff argument gives an age of order $10^9$ years, with its fuel fraction and mass-luminosity assumptions explicitly stated. It does not use a modern fitted Hyades age or a full stellar isochrone. Unresolved binaries, extinction and deviations from the homology law affect the estimate.
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