Why is 3-chloro-5-(1-methylethenyl)cyclopenta-1,3-dien-1-ol named so?
The most important simplified criteria for the numbering are:


lower locants for the group that is expressed as suffix
lower locants for multiple bonds
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name


The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:


  P-14.4 NUMBERING
  
  When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
  
  (…)
  
  (c) principal characteristic groups and free valences (suffixes);
  
  (…)
  
  (e) saturation/unsaturation:
  
    (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  
    (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
  
  (f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
  
  (g) lowest locants for the substituent cited first as a prefix in the name;
  
  (…)


The principal characteristic group of the compound that is given in the question is the $\ce{-OH}$ group. It is expressed as the suffix “-ol”. According to Rule (c), a low locant is assigned first to this group, i.e. “-1-ol”.

In the next step, low locants are assigned to the double bonds according to Rule (e), i.e. “cyclopenta-1,3-dien-1-ol”.

That leaves only one possible locant set for the remaining substituents, i.e. “3-chloro” and “5-(prop-1-en-2-yl)”. The rules (f) and (g) are not needed to make a decision.

Therefore, the complete name for the compound that is given in the question is 3-chloro-5-(prop-1-en-2-yl)cyclopenta-1,3-dien-1-ol.



Note that the preferred prefix for the “isopropenyl” or “1-methylethenyl” (completely: “1-methyleth-1-en-1-yl”) is now “prop-1-en-2-yl”.