Before the emergence of the modern chess problem in the mid-19th
century conditional problems were common, and this is one of the
best examples. The mating check must be delivered by the pawn.
My apologies to solvers. I took the problem from a source which gave an
incomplete stipulation. The proper stipulation should read “Mate in 5 with
the pawn, without capturing the rook”.
Solution: With Black ready to capture the pawn it would appear
that a sequence of checks is called for, so after 1.Qc8+
Rb8 the quiet continuation 2.Ke7 is not so easy to
spot. There follows 2...Rxc8 3.Bg2+ Kb8 4.Ba7+ Kxc7
5.b6 mate. Without the condition forbidding capture of the
rook there is a mate in 4 by 1.Qa4+ Kb8 2.Rc8+ Kb7 3.Qa6+ Rxa6
4.bxa6 (or 1...Ra6 2.Rc8+ Kb7 3.bxa6.) My thanks to the solvers
who pointed this out.