#### Answer

Option $A$

#### Work Step by Step

With $x$=unknown number, then
"seven times a number" = $7x$
"the difference between seven times a number and 9" = $7x-9$
while
"the sum of a number and 2' = $x+2$
"five times the sum of a number and 2" = $5(x+2)$
Since
"the difference between seven times a number and 9" is equal to "five times the sum of a number and 2"
then,
$7x-9=5(x+2)$
Therefore, the equation needed to solve the given problem is the one in Option $A$.