Ok for C13 NMR, you need to find the number of different carbon atoms. For 1,5-dichloropentane, you see that there is a chlorine attached to the 1-carbon and the 5-carbon (see the attached picture for reference).
So just by looking at this structure, do you notice that carbons 1 and 5 are the same? They both have a chlorine attached to them, and they both have 3 carbons between each other (carbons 2,3, and 4).
Now if you look at the other carbons (2,3,4) they have no atoms bonded to them. However, by looking at carbons 2 and 4, you will notice they are the same. Why? Because both are next to a chlorine-bonded carbon, and both have a carbon between them (carbon 3).
As for carbon 3, it is not similar to any of the carbons, so it will register its own peak.
Therefore, you should see a total of 3 peaks for this C13 NMR.
Peak 1- A result of carbon-1 and carbon-5 with the chlorines
Peak 2- A result of carbon-2 and carbon-4, which are next to the chlorine carbons
Peak 3- A result of carbon-3, which has no other similar carbons.
Remember, whenever you see a peak in NMR, it doesn't mean that this peak is the result of a single carbon atom. This peak could be the result of 2,3 or even 5 carbon atoms, but the thing is they are all the same (meaning they have the same bondage).
I'm sorry if this did not explain it properly. PM me if you have further questions.
