I came across a reaction whereby a 1-5 dicarboxylic acid is converted to lactone with SOCl2. I was wondering what the mechanism of this was.

I know that SOCl2 converts carboxylic acids to acyl chlorides. Is it the case that one carboxylic acid undergoes this transformation, then the oxygen from the OH of the other carboxylic acid attacks the acyl chloride, making the Cl a leaving group?

Is this the case or am I missing something?

Thank you.