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in six…
Pretty idea.
1. Rc1+ Kb8 2. Qb4+ Kh8 3. Bf3+ Rxf3 4. Qe4+ Qxe4 5. Rc8++
Force black’s king into the corner, then remove defenders from the back rank for a rook mate:
1. Rc1 Kb8
2. Qb4 Ka8
3. Bf3 Rxf6
4. Qe4 Qxe4
5. Rc8#
The first poster has correctly pointed out that black can stall for another move:
4. … Rd5
5. Qxd5 Qc6
6. Qxc6#
or
4. … Rd5
5. Qxe8 rd8
6. Qxe8#
This problem appears to be flawed. The mate takes six moves:
1. Rc1+ Kb8
2. Qb4+ Ka8
3. Bf3+ Rxf3
4. Qe4+
Now:
4. … Kb8 (or 4. … Rd5)
5. Qxe8+ Rd8
6. Qxd8#
(Note that in the second case, 5. Qxd5+ postpones it by one more move, like:
5. Qxd5+ Qc6
6. Qxc6+ Kb8
7. Qb7#