Seeing the mating idea for White is a little harder here, but it should give you no trouble if you look at how White’s pieces bear on Black’s king and especially at any checks you can give. The knight at f5 can give a check from e7, forcing Black’s king back to h8; and now with no defenders along his back rank Black gets mated with RxN—almost. The impediments are (a) Black’s bishop at b4, which guards e7 and f8, and (b) the knight on f6, which can be interposed on g8. Begin with the bishop. When you see a long line like this between guardian and mating square, consider obstructing it. White can insert his dark-squared bishop onto the diagonal with Bc5; the queen behind the bishop, on f2, provides the protection needed to stop Black from erasing the blocker with BxB. White imagines the sequence thusly: 1. Bc5, BxB; 2. QxB, b6xQ; then the mating finale 3. Ne7+, Kh8; 4. RxN+, Nf6-g8; 5. RxN#.

That is the ideal sequence. Of course Black is unlikely to cooperate in such docile fashion; the point is to realize that if he makes all of his natural captures and recaptures he will end up mated. This means that if he is alert he will have to forgo one of those captures, and that the sequence instead will only win material. What is Black’s actual reply to Bc5 likely to be? Probably Nf6-d7—forfeiting his bishop to BxB and instead bringing in a fresh guard for f8.

A loose end: when you plan an offensive sequence you have to be mindful of any checks your opponent can throw into the mix, possibly seizing the initiative and spoiling your plans. Here Black can try 1. ...Qa1+, but it’s met with Bf1 and so doesn’t change anything. Another loose end: after 1. Bc5, BxB; 2. QxB, Black can skip the capture of White’s queen and instead play Nd7, again beefing up the protection for f8. But now it’s too late to avoid mate, as becomes clear if you are resolute in examining your checks: 3. QxNf8+, NxQ; and now, of course, 4. Ne7+, Kh8; 5. RxN#.