How to compute the Weyl Character Formula

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I am asked to find the character of the standard representation of $SO(2n+1)$ when restricted to the standard maximal torus using the Weyl character formula. I know, from the representation, that this will be simply $\sum_{k=1}^n 2\cos(\theta_k) +1$, but I have no idea how to begin to use the formula, which I am pulling from this wiki.

If I could get an explanation for how to compute it for a smaller case like $SO(5)$ so I could get an idea, that would be really helpful. I have already computed the highest weight, the half-sum of positive roots and the Weyl group. Actually computing the exponentials is confusing me.