trigonometry - Limit of $lim limits_{x to frac{5π}{2}^+} frac{5x - tan x}{cos x}$

So I have the following problem:

$$\lim \limits_{x \to \frac{5π}{2}^+} \frac{5x - \tan x}{\cos x}$$

I can't figure out how to get the limit. I tried splitting it up to:

$$\lim \limits_{x \to \frac{5π}{2}^+} \Big(\frac{5x}{\cos x} - \frac{\tan x}{\cos x}\Big)$$

I'm lost and unsure of what to do next. I'm taking a Calc 1 class and we have not yet gotten to L'hopitals and other methods yet (and also I am not sure how I could incorporate those ideas either).