Allport and Cattell believed we were all born with five core personality traits

Allport and Cattell believed we were all born with five core personality traits

Allport and Cattell believed we were all born with five core personality traits:  openness, conscientiousness, agreeableness, extroversion, and neuroticism.  If these five, as you pointed out above, neuroticism is most closely associated with anxiety.  Therefore, they believed that if one was born into a family where neuroticism was high, chances are the person could have higher levels of anxiety verses those who were born in families where neuroticism was low.  Do you agree?