Использование NSDateComponents
NSDate *today = [NSDate date];
NSCalendar *gregorian = [[[NSCalendar alloc] initWithCalendarIdentifier:NSGregorianCalendar] autorelease];
NSDateComponents *offsetComponents = [[[NSDateComponents alloc] init] autorelease];
[offsetComponents setDays:-5];
NSDate *fiveDaysAgo = [gregorian dateByAddingComponents:offsetComponents toDate:today options:0];
, чтобы преобразовать его в строку с предпочтительным форматом, используйте NSDateFormatter
NSDateFormatter *dateFormatter = [[[NSDateFormatter alloc] init] autorelease];
[dateFormatter setDateFormat:@"yyyy-MM-dd"];
NSString *formattedDateString = [dateFormatter stringFromDate:fiveDaysAgo];