I do NOT want to know what would happen otherwise...

Total number of ways in which $5$ people can leave at $5$ floors = $5^5$

For the exceptional ways of leaving the elevator, we have to consider all the ways in which a pair (a M and a F) can leave at the upper floors while remaining $3$ people have left the elevator at the lower floors.

There are $6$ ways to choose a pair out of $3$ M and $2$ F.

For a given pair, the number of exceptional ways in which they can leave are as follows:

case $1$ :

Total exceptional ways in which each member of pair leaves at $5^{th}$ floor =

Number of ways in which the remaining $3$ people can leave at $4^{th}$ to $1^{st}$ floors = $4^{3}$

case $2$ :

Total exceptional ways in which each member of pair leaves at $5^{th}$ to $4^{th}$ floor such that at least one of them leave at $4^{th}$ floor =

Number of ways in which the remaining $2$ people can leave at $5^{th}$ to $4^{th}$ floors (excluding ways already considered in case $1$ ) times Number of ways in which the remaining $3$ people can leave at $3^{rd}$ to $1^{st}$ floors = $3 \times 3^{3}$

case $3$ :

Total exceptional ways in which each member of pair leaves at $5^{th}$ to $3^{rd}$ floor such that at least one of them leave at $3^{rd}$ floor =

Number of ways in which the remaining $2$ people can leave at $5^{th}$ to $3^{rd}$ floors (excluding ways already considered in case $1$ and $2$ ) times Number of ways in which the remaining $3$ people can leave at $2^{nd}$ to $1^{st}$ floors = $5 \times 2^{3}$

case $4$ :

Total exceptional ways in which each member of pair leaves at $5^{th}$ to $2^{nd}$ floor such that at least one of them leave at $2^{nd}$ floor =

Number of ways in which the remaining $2$ people can leave at $5^{th}$ to $2^{nd}$ floors (excluding ways already considered in case $1$ , $2$ and $3$ ) times Number of ways in which the remaining $3$ people can leave at $1^{st}$ floors = $7 \times 1^{3}$

Total number of ways = $5^{5} - 6(4^{3} + 3 \times 3^{3} + 5 \times 2^{3} + 7 \times 1^{3}) = 1973$

PS: Sorry for the typos (if any).