Let's simplify the equation step by step:

(7x + 1) - (9x + 3) = 5
We can distribute the negative sign inside the parentheses:
7x + 1 - 9x - 3 = 5
Now, combine like terms:
(7x - 9x) + (1 - 3) = 5
-2x - 2 = 5
Next, add 2 to both sides of the equation to isolate the variable term:
-2x = 7
Finally, divide by -2 to solve for x:
x = -7/2 or x = -3.5

Therefore, the solution to the equation is x = -3.5 or -7/2.