Final answer:
The false statement is that both estrogen and testosterone exert local positive feedback on cells in the gonads, as this generally only occurs with estrogen during the midpoint of the menstrual cycle.
Step-by-step explanation:
The false statement regarding similarities between estrogen and testosterone is that both hormones exert local positive feedback on cells in the gonads, or statement 5 in the initial list. In actuality, high levels of estrogen can create a positive feedback loop but only during the midpoint of the menstrual cycle, leading to an LH surge that triggers ovulation. Conversely, these hormones typically exert negative feedback on the secretion of LH, FSH, and GnRH to maintain hormonal balance. Both testosterone and estrogen do stimulate the development of secondary sex characteristics, and both are indeed secreted by the gonads.