Lady Philosophy says, "... there is naturally implanted in the minds of men the desire for the true good, even though foolish error draws them toward false goods"; what are three of five false goods that she lists, and why can't these goods cure anxiety or satisfy despair?

We need to look at Book 3 to find Lady Philosophy's advice on false goods and the attainment of happiness. She says that a true good would make the attainer so happy that he would not be able to desire anything further, because that good would contain all other goods "within itself." She then lists several goods which men have, falsely, thought to be the highest.
The first of these, essentially, is money—Lady Philosophy says that some people are so geared towards "needing nothing" that they work and work to acquire wealth.
Next, some people want civic honors, respect, and veneration from those around them.
Third, some people want power, in two forms:
1. Ruling outright.2. Being close to those who are in power.
Others want celebrity and fame and will try to achieve this in either wartime or peacetime by various methods.
She then explains some people seek one of these goods in order to attain another—for example, they want to be rich so they can be powerful, or they want to be powerful so that they can be rich and famous. Essentially, they want pleasure.
If the five goods are wealth, honors, power, glory, and pleasure, then, the problem with these is that they are all lesser goods. What humans really want to attain is happiness. Having selected whatever good appeals to them, humans are all actually striving towards the same thing, and they will not be satisfied until they achieve true happiness. Some will strive for one of these false goods in order to attain another, exactly because they feel that this is the quickest path to happiness. But because the first good they targeted did not contain happiness within itself—it was not complete—it could not possibly be the highest good, happiness itself, because the person who attained it was still able to desire more.
In section 3, Lady Philosophy goes on to describe in more detail some of the unhappinesses which might befall those who have acquired these false goods.
1. The rich man may become anxious or distressed because he feels that he has more than he should as others have not enough. At the same time, he is concerned with the need to "guard" his money. So, he is not made happy by his wealth.
2. The man who achieves honors is likely to be subject to more scrutiny. As such, it is likely that his disgraces will be unveiled, and he will become accused of dishonesty. Meanwhile, other dishonest people are often lifted to these honored positions, which then become dishonorable by association.
3. The man who becomes powerful is in danger always of becoming a tyrant, just as many monarchs have "changed happiness to calamity." Power often "ruins" those who have it, and stirs up dissent among those who do not.
You can look at sections 5 and onwards in this book to find Lady Philosophy's discussions of the other false goods.