The simplest way to solve this is with the sine rule.
A/sin(a) = B/sin(b) = C/sin(c)
where A, B, C are the lengths of the sides and a,b and c are their opposite angles.
Remember also that the sum of the angles in a triangle = 180°
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So the missing angle is 45° (=180-71-64).
Therefore, 5/sin(45) = B/sin(71) = C/sin(64)
Therefore, B = 6.6858259654412220511751510867703
and C = 6.3554336502823673953106682165706
Al.