= Solution
With the proximity-resolution convention $w=k\sqrt{\lambda g}$, the maximum mask-wafer gap is
$$
\boxed{g_{\max}=\frac{w^2}{k^2\lambda}}.
$$
For $w=5\,\mu\mathrm m$ and $k=2$, \b[$g_{\max}\simeq17.1\,\mu\mathrm m$ at $365\,\mathrm{nm}$]. If the g-line is used instead, \b[$g_{\max}\simeq14.3\,\mu\mathrm m$ at $436\,\mathrm{nm}$]. The wavelength must be specified; the question's preceding choice of two lamp lines does not select a unique number. This estimate neglects extra loss of resolution from finite resist thickness, mask imperfections and angular illumination spread.
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