Bayes law and risk ratio

I understand Bayes' law. However, I'm struggling to intuitively grasp it in the context of cancer screening.

For instance, say you are trying to find out the probability of someone having cancer given that he is tested positive P(C|+). Bayes law says that P(C|+) = P(C) * [P(+|C) / P(+)].

So if he is a healthy adult, with say a baseline of 5% chance of having cancer. A positive test will elevate his baseline 5% by x times, where x = P(+|C) / P(+).

How do I intuitively draw the link between P(+|C) / P(+) and the x times elevated risk in light of the positive test result?

Thanks in advance!