Let AB = BC = CD = 1
Use Sine Law and isosceles triangle BCD to calculate BD (you should get ~1.992)
Do you see that angle ABD = 65 (70 - 5) ?
Use Cosine Law and triangle ABD to calculate AD (you should get ~1.813)
We now have BD / sin(A) = AD / sin(65)
From that, calculate angle A (you should get 85 degrees.
If you draw a diagram, it'll be easier for you to follow above steps.