Configurations of Reactants in Second Order Nucleophilic Substitutions
I tried to pinpoint you in the right direction through comments, but apparantly I failed. The bottom line is that the molecule you drew and the one in the textbook answer are identical. Here’s why:



In the top row, you can see the (S)-2-chloropentane, which I have drawn as you have on the left, slowly rotating around an axis equivalent to the reaction arrows to give you the same molecule drawn in a different orientation.

Now, if you do an $\mathrm{S}_{\mathrm{N}}2$ reaction, all you need to do is replace the chlorine atom and invert the stereochemistry which I have done for both cases. You can now see that both sides are identical.

It does not (and must not) matter whether you draw the 2-chloropentane with the substituted carbon to the right or to the left. Both ways are identical. Usually, you will chose an orientation that is consistent with further or earlier steps of your synthesis, but if you only have one one reaction that point is moot. (It matters a lot more in total synthesis, where it helps to draw reactands in a way that show their conformation in the final molecule.) Furthermore, there is a IUPAC style guide out there somewhere, which probably says one of the two ways is to be preferred if no other reasons speak for the other … but that’s more relevant for journal publications, not for practising or for exam answers.

So just for total consistency’s sake: Everything you did was correct; just remember that molecules can be drawn with different orientations, and learn to turn them around before your inner eye.