Your question has two components: 1) Whether to write out the number as a numeral or in words, and 2) whether to indicate "dollars" in words or with a symbol.
I did not find a direct answer or example in the manual, but a discussion on the APA style blog may provide some guidance:
To address issue one, look at the question in the comments sectiom (comment #7 from the top) where a student asks about the proper way to write about an approximate number of people. The author of the style post states that the correct answer is "Almost 3,000,000 people." She provides the explanation that because 3,000,000 is larger than 10, is should be written as a numeral. She does not comment on the issue of this being an approximate amount, but because the question is about an approximate number of people, it seems she interprets the exception to rule 4.31e as only pertaining to the units of time listed in the exception. Also, note that in the body of the blog post, the author refers to approximate units of time rather than approximate numbers in general.
To address issue two, look further in the comments section, at the bottom two comments on the page. Here, someone asks how to write about an amount of money that is less than $10. The author notes that in prose, she would recommend writing out the word "dollars," while in tables or with mathematical operators, it might be more appropriate to use the symbol (referring to rule 4.45 about describing statistics in text).
In sum, this discussion seems to indicate that "I have about 5,000,000 dollars" would be the correct form. The number would be written in numerical form because a) it is over 10 and b) it is not an approximate amount of time. The unit of money ("dollars") would be written in prose text and appear as a symbol on tables or when discussing mathematical operations.