How do I check mate this?
If it's black's move, it's very simple - so simple that I would suggest you put in the effort yourself.
1. Rf3 Bxf3 2. Qxc7 Kxc7 3. Bf4+ Kd7 4. Bg5 Rh8+ 5. Bh4 Rxh4#
You can also start off with the Queen sacrificing herself to delay the inevitable, but those lines also lead to mate in five.
(I recommend you put such queries in the chess analysis - and hope it's not a game you're playing against someone now?)