Given that it appears impossible to make the set out of linear combinations of its elements, why is it still dependent? The answer key says the following set of functions is linearly dependent:
$\{5, \cos^2x, \sin^2x\}$.
Without calculating the Wronskian, I would've guessed it was independent because there's apparently no way you can form a linear combination out of any of these functions to get others: you can't multiply $5$ to get $\cos x$; you can't multiply $\cos x$ to get $\sin x$, etc. What's wrong with my reasoning? 

Hint:
$$
5 \cos^2 x+ 5\sin^2x=5
$$
