Conditional complexity code smell is about complex large conditions that tend to grow larger and more complex with time. This code smell can be refactored with the strategy design pattern. As the strategy design pattern deals with many related objects, there is scope for using the Factory method, and the null object design pattern can be used to deal with unsupported subclasses in the Factory method: 

//Before refactoring
void SomeClass::someMethod( ) {
      if (  ! conition1 && condition2 )
         //perform some logic
      else if ( ! condition3 && condition4 && condition5 )
         //perform some logic
      else
         //do something 
} 

//After refactoring
void SomeClass::someMethod() {
     if ( privateMethod1() )
          //perform some logic
     else if ( privateMethod2() )
          //perform some logic
     else
         //do something
}