What should be the name of this substituted cyclopentane?
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the preferred suffix for the principal characteristic group $\ce{{}-CN}$ is ‘carbonitrile’. Therefore, the name of the parent structure of the compound given in the question is ‘cyclopentane-1-carbonitrile’ (note that the locant ‘1’ would be omitted in monosubstituted homogeneous monocyclic rings, i.e. ‘cyclopentanecarbonitrile’).

The relevant rules for the numbering of locants for the four substituent prefixes (‘amino’, ‘bromo’, ‘chloro’, and ‘hydroxy’) are:


  P-14.3.5 Lowest set of locants
  
  The lowest set of locants is defined as the set that, when compared term by term with
  other locant sets, each cited in order of increasing value, has the lowest term at the first
  point of difference; (…)


and


  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:
  
  (…)
  
  (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;
  
  (…)


Note that Rule (f) takes precedence over Rule (g).

In accordance with Rule (f), the compound given in the question could be named as 2-amino-4-bromo-3-chloro-5-hydroxycyclopentane-1-carbonitrile as well as 5-amino-3-bromo-4-chloro-2-hydroxycyclopentane-1-carbonitrile since both names correspond to the locant set ‘2,3,4,5’. However, according to Rule (g), this example is named as 2-amino-4-bromo-3-chloro-5-hydroxycyclopentane-1-carbonitrile rather than 5-amino-3-bromo-4-chloro-2-hydroxycyclopentane-1-carbonitrile since ‘amino’ is cited first as a prefix in the name.