Do the first five consciousnesses have the mental factor of mindfulness?

Question: Memory is a dharma-object seed stored in the tathāgatagarbha; the object-aspects of the first five sense-objects cannot be stored, because the object-images recalled can only correspond with the mind consciousness, and the first five consciousnesses have no mental factor of recollection (smṛti), so they cannot discern the recalled object-images, right?

Answer: All dharmas can be stored as seeds. All bodily, verbal, and mental actions, and all the people, events, objects, and principles one has experienced—that is, the entire realm of the six sense-objects—are all stored by the tathāgatagarbha as seeds. Afterwards, when the manas grasps at, deliberates, and seeks to discern, the tathāgatagarbha, in accordance with the manas's mental factor of volition (cetanā), transmits the seeds out to become mental objects (dharma-viṣaya), becoming a subjectively imagined realm. After the manas has taken this as its object, if it wishes to discern in finer detail, the tathāgatagarbha gives rise to the solitary consciousness (mano-vijñāna-eka-citta) to discern each one—this is what is called recollection. Therefore, recollection contains details; the realm recalled belongs to mental objects, which the five consciousnesses cannot discern. The object-aspects of the first five sense-objects are also stored in the tathāgatagarbha as seeds and as a kind of information; seeds and information are formless and without appearance, and do not belong to the realm of the five sense-objects. When the causes and conditions are complete, the tathāgatagarbha, in accordance with the seeds, also outputs the five sense-object realms, and then, following the manas's mental factor of volition, the tathāgatagarbha gives rise to the six consciousnesses to discern them; however, this no longer counts as recollection. The five consciousnesses also possess the five object-specific mental factors: desire (chanda), determination (adhimokṣa), recollection (smṛti), meditative concentration (samādhi), and wisdom (prajñā); therefore, the five consciousnesses do have the mental factor of recollection.