To evaluate this expression, we can use the trigonometric identities:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Given that the expression is cos(125)cos(5) + sin(55)cos(85), we can rewrite it as:

cos(125+5) + sin(55+85)

Which simplifies to:

cos(130) + sin(140)

Now we can find the values of cosine and sine of 130 and 140 degrees using a calculator:

cos(130) ≈ -0.6428
sin(140) ≈ 0.6438

Substitute these values back into the expression:

-0.6428 + 0.6438 ≈ 0.001

Therefore, the value of the expression is approximately 0.001.