There are multiple steps to solve this problem.
First, we need to find x. The Pythagorean theorem is a^2+b^2=c^2. Substitute the the sides of the triangle into the equation.
x^2+8^2=(x+5)^2
Square everything.
x^2+64=x^2+10x+25
Subtract x from both sides.
64=10x+25
Subtract 25 from both sides
39=10x
Divide both sides by 10
x=3.9
The formula for the area of a triangle is 1/2*b*h. The base of this triangle is 8 and the height is 3.9.
Substitute the values into the formula.
1/2*8*3.9
Simplify
1/2*31.2
15.6
The area of the triangle is 15.6 units^2