= Solution
The <transition matrix> over five years is $P(5)=e^{5Q}$. Its first row conditions on starting in state 1. The displayed approximate probabilities mean that, five years later, about \b[65% remain disease-free, 6% have local recurrence only, 10% have distant metastasis only, 2% have both, and 16% have died]. They are probabilities of the states occupied at five years; they are not the probabilities of the next jump destinations or annual <transition intensities>. In particular the positive <probability> of state 4 does not require a direct $1\to4$ arrow: the paths $1\to2\to4$ and $1\to3\to4$ contribute to it. The <probability> of death includes deaths after any allowed sequence of intermediate states.
The printed row sums to $0.99$ rather than one because the entries are approximate; an exact stochastic transition row sums to one. Exponentiating the displayed three-decimal generator gives approximately $(0.65377,0.06490,0.09775,0.02532,0.15826)$, illustrating that the edited, low-precision table should not be treated as an exact matrix exponential of its separately rounded rates.
State 5 is an <absorbing state>, so once entered it can never be left. Its generator row is zero, and the last row of every positive-time <transition matrix> is therefore
$$
\boxed{(0,0,0,0,1).}
$$
This explains all four leading zeroes in the printed last row.
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