  (New version with some expanded discussion; figures and minor typos
corrected.)
  We have calculated the contribution proportional to the fifth power of the
pion mass in the chiral expansion of the nucleon mass in two flavour HBCPT.
Only one irreducible two-loop integral enters, and this vanishes. All other
corrections in the heavy-baryon limit can be absorbed in the physical
pion-nucleon coupling constant which enters in the third order term, and so
there are no contributions at fifth order. Including finite nucleon mass
corrections, the only contribution agrees with the expansion of the
relativistic one-loop graph in powers of the ration of the pion and nucleon
masses, and is only 0.3% of the third order term. This is an encouraging result
for the convergence of two-flavour heavy-baryon chiral perturbation theory.
