Which is the correct name: 2,3-dimethyl cyclopentene or 1,5-dimethyl cyclopentene?
The correct name is 1,5-dimethylcyclopent-1-ene. The double bond has the highest priority and so these two carbons must be numbered 1 and 2 if possible (yes in this case because the molecule is cyclic). We then have to choose between numbering the methyl substituents 1,5 or 2,3. The lowest locant sum rule that you mentioned doesn't actually exist, even though it is often taught. It is a agglomeration of several rules which works most, but not all of the time. The actual rule we are interested in is the first point of difference rule which states:


  2.2 - The longest chain is numbered from one end to the other by Arabic numerals, the direction being so chosen as to give the lowest numbers possible to the side chains. When series of locants containing the same number of terms are compared term by term, that series is "lowest" which contains the lowest number on the occasion of the first difference. This principle is applied irrespective of the nature of the substituents.


Therefore the locant set 1,5 is lower than the locant set 2,3 since at the first point of difference, 1 is lower than 2.