Solution:

Convert each letter to a digit in base $6$: $I \mapsto 0$, $N \mapsto 1$, $P \mapsto 2$, $R \mapsto 3$, $T \mapsto 4$, $U \mapsto 5$. Then the dictionary simply consists of all base-$6$ integers from $00000_{6}$ to $55555_{6}$ in numerical order. If one number can be obtained from another by a rearrangement of digits, then the numbers are congruent modulo $5$ (this holds because a number $a^{a b c d e_{6}} = 6^{4} \cdot a + 6^{3} \cdot b + 6^{2} \cdot c + 6 \cdot d + e$ is congruent modulo $5$ to $a + b + c + d + e$), but if there are $100$ other numbers between them, then their difference is $101$, which is not divisible by $5$. So there are no such pairs.