How is it possible that his five senses are still working? How can he even talk?
In short it is because of the Yomi Yomi no Mi Fruit's power he is able see, taste and do other things.
According to wiki:
Through the fruit's powers, Brook is able to function without the presence of necessary and vital body parts that have decomposed long ago. He is able to interact with the environment around him without the presence of eye balls or any other sensory organ to aid him. He, in particular, retains his ability of speech despite his vocal chords and even his windpipe have long since rotted away. He is able to taste and digest food like any other normal living thing to sustain himself. Drinking milk in particular heals him as the calcium intake repairs any of Brook's bones that may have been broken in battle. Depending on the situation, Brook is also able to produce organic matter such as tears, fecal matter, and even blood from his nose despite not having any organs nor bodily liquids to produce such matter.