It has long been my opinion that Sections 5.3, 5.4, and 5.5 are the most rewarding and also the most challenging part of this course. Conditional probability is an extremely useful concept, and applying the concept leads to some very interesting and useful techniques. Good examples abound. For example, if you test positive for a disease of some sort, how likely is it that you actually are infected as opposed your case simply being an instance when the test result is wrong? If you have enough data on the incidence of the disease and the accuracy of the test, you now know how to answer that sort of question.
The remaining topics in Part 5 are a bit more straight forward (independence, independent trials, and expected value). Then Part 6 will be an application of probably that reconnects to what we learned about matrices in Part 1. You'll soon be in the home stretch.