Using the sine rule, a/sin(A) = b/sin(B) = c/sin(C)
But we have to have at least two angles and two lengths to equate it to one another. We could find the third angle in this triangle to use as our second angle, but we do not know the value of x, so we have to find the second length.
To do that, we use Pythagoras theorem;
a^2 = b^2 + c^2
a^2 = 7^2 + 5^2
a^2 = 49 + 25
a^2 = 74
square root both sides to get rid of the square on a:
a = sqrt(74)
a ~ 8.60
Now we can apply our sine rule. Note that the lengths and angles are the ones opposite each other. For example, the corresponding angle of 8.60 is 90° and the one for 5 is x°.
So,
8.60/sin(90) = 5/sin(x)
8.60/1 = 5/sin(x), since sin(90) = 1
Make sin(x) the subject,
sin(x) = 5/8.60
sin(x) = 0.5814
x = sin^-1(0.5814)
x ~ 35.6°