This question involves solving permutation equations using the formula ⁿPᵣ = n!/(n-r)!. The key is to expand both sides using factorial notation, cancel common terms, and solve the resulting quadratic equation. For both parts, we must ensure r $\leq$ 5 since we have ⁵Pᵣ, and r $\geq$ 1 for the permutation to be valid.