one light - 2 light switches?

I am attempting to fit a new light fitting, expecting it to be straight forward. But the light either remains permanently on or permanently off - ie. the switch isn't working.

Coming from the ceiling I have two reds, two black and one earth.

I'd assumed that I should connect both red wires to the live terminal on the new light fitting and the black wire to the neutral. But, as I said, this results in the light being constantly on.

Any thoughts or suggestions would be appreciated.

Thanks.