Start by using the FOIL method to expand the two parantheses
(x+3)(x+4) = x^2 + 3x + 4x + 12 = x^2 + 7x + 12
Your equation now becomes
x^2 + 7x + 12 = 5
Rearrange so that all the terms are on one side of the equation
x^2 + 7x + 7 = 0
You can solve this quadratic equation by using the quadratic formula
x_(1,2) = (-7 +- sqrt(7^2 - 4 * 1 * 7))/(2 * 1)
x_(1,2) = (-7 +- sqrt(21))/2 = {(x_1 = (-7 + sqrt(21))/2), (x_2 = (-7 - sqrt(21))/2) :}
Check to see if these values are actual solutions
((-7 + sqrt(21))/2 + 3) ((-7+sqrt(21))/2 + 4) = 5
((-7+sqrt(21))/2)^2 + 7 * ((-7 + sqrt(21))/2) + 12 = 5
(49 - 14sqrt(21) + 21)/4 + (-49 + 7sqrt(21))/2 = -7
70 - color(red)cancelcolor(black)(14sqrt(21)) - 98 + color(red)cancelcolor(black)(14sqrt(21)) = -28
-28 = -28 -> x_1 is a valid solution!
Now check for the second solution
((-7-sqrt(21))/2)^2 + 7 * ((-7 - sqrt(21))/2) + 12 = 5
(49 + 14sqrt(21) + 21)/4 + (-49 - 7sqrt(21))/2 = -7
70 + color(red)cancelcolor(black)(14sqrt(21)) - 98 - color(red)cancelcolor(black)(14sqrt(21)) = -28
-28 = -28 -> x_2 is a valid solution as well!
