The 5th case-affix is used optionally when the noun expresses an attribute, being the cause of an action and not being of the feminine gender.,
Ex. जाड्येन जाड्यताम् वा बद्धः 'he has been bound by reason of his dullness.' पांडित्येन or पांडित्याद् मुक्तः 'saved through learning.'
Guna-vachana nouns are generally abstract nouns. Therefore not here धनेन कुलम्. If an abstract noun is of feminine gender, this rule will not apply, as वुद्ध्या or प्रज्ञया मुक्तः 'he was set at liberty on account of his skill or wisdom.',