If 5° $$\leq$$ x° $$\leq$$ 15°, then the value of sin 30° + cos x° - sin x° will be :

For smaller values of 'x', cos 'x' will be close to 1 and sin x will be close to 0. 
Sin 30° = 1/2 = 0.5
As we move closer to 0, the value of cos x increases and sin x decreases. Therefore, when we move from a larger value of x to a smaller value, the value of the expression cos x - sin x will increase. 

Let us evaluate the value of the expression at x= 30° (since we know the values of cos x° and sin x° at this point) and then logically deduce the range of the value of the expression. 

At x = 30°, cos x = $$\frac{\sqrt{3}}{2}$$ and sin x = $$\frac{1}{2}$$
Therefore, cos x° - sin x° would have been 1.732/2 - 0.5 = 0.866 - 0.5 = 0.366

sin 30° + cos x - sin x will be 0.866

At x = 0, sin 30 + cos x - sin x will be 0.5 + 1 - 0 = 1.5.
At x = 5°, the value of the expression sin 30 + cos x - sin x  will be slightly less than 1.5. 
Therefore, we can infer that the upper limit of the expression will be greater than 1. None of the given limits include values greater than 1. Therefore, option E is the right answer. 

Alternate solution:

The value of sin 15° and cos 15° can be found out using the identities sin (A-B) = sin A cos B - cos A sin B and cos (A-B) = cos A cos B + sin A sin B.
Substituting A = 45° and B = 15° in these expressions, we get, 
sin 15° = 0.2588
cos 15° = 0.9659

sin 30° + cos 15° - sin 15° = 0.5 + 0.9659 - 0.2588 = 1.2071.
None of the given options capture this value in the range. Therefore, option E is the right answer.