= Solution
The unique dimension-five operator built solely from Standard Model fields is the <Weinberg operator>
$$
\frac{c_5}{\Lambda}(L^iH^j)\epsilon_{ij}(L^kH^\ell)\epsilon_{k\ell}+\mathrm{h.c.},
$$
which gives a <Majorana mass term> $m_\nu\sim c_5v^2/\Lambda$ after the Higgs condenses. A dimension-six example that mediates <proton decay> is
$$
\frac{c_6}{\Lambda^2}\epsilon_{abc}(Q^aQ^b)(Q^cL),
$$
with Lorentz and weak indices contracted appropriately; $u^cu^cd^ce^c/\Lambda^2$ is another. Their dimensions explain why neutrino masses are tiny and proton decay is rare: both probe a high scale, while the stronger proton-lifetime bound places especially severe constraints on baryon-number violation.
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