Step 1: Understanding the Concept
Cerebrospinal fluid fills the brain ventricles, the central canal and the space around the brain. It is a clear and slightly alkaline fluid.
Step 2: Recall the value
CSF is mostly water with very few proteins and cells, so it is only slightly denser than water. Its specific gravity is about 1.005.
Step 3: Why the other values fail
A specific gravity of 1.05 or 1.5 would mean a much denser fluid, which CSF is not.
Final Answer:
The specific gravity of CSF is 1.005.
\[ \boxed{\text{(B) }1.005} \]