Some Trig Help: Find the exact value of cos(−5pi/12)

I've used the sum and difference identity for cos and here is my answer:

Cos -5pi/12 I translate as -75 degrees, so I used my known angles which were:

**pi/-6** and **-pi/4**.

I also know that -5pi/12 is in the **4th region** so the value should be positive (**A**ll **S**tudents Take **C**alculus).

From the Cosine Sum formula we have:

Cos(a+b)=Cos(a)Cos(b)-Sin(a)Sin(b)

Cos(-pi/4 + -pi/6)= Cos(-pi/4)Cos(-pi/6)-Sin(-pi/4)Sin(-pi/6)

Cos(-pi/4 + -pi/6)=(sqrt2/2)(sqrt3/2)-(sqrt2/2)(1/2)

.....

So what Did I do wrong guys?