| | Re: Which tense(s) is/are correct?
First of all, distinguish between verb forms and tenses. English only has two tenses - present and past - but also has three forms of aspect - simple, progressive (or continuous) and perfect.
So - in these verb forms you need to ask yourself a) what does the tense (present or past) indicate? and b) what does the aspect indicate?
Let's take the easiest ones first
1c) Over the last five weeks, Joe earned $5000.
(2c) Over the last six months, May wrote ten essays.
Here the speaker perceives both the time period and the events (earning and writing) as past and finished. It might be said for example at the beginning of August and the context might be something like...
2c) Mary has to submit her next essay on August 31st, but it shouldn't be a problem. She wrote ten between February and the end of July, and if she managed to write ten over the last six months a complete month should give her plenty of time for just one.
(1a) Over the last five weeks, Joe has earned $5000.
2a) Over the last six months, May has written ten essays.
Here the aspect is perfect simple, indicating that the speaker sees the event (earning/writing) as complete/finished - ie Joe has earned a total of $5,000 and Mary has written a total of 10 essays (probably one after the other) in the time period. However, the tense is present - indicating that the time period is seen as including both past and present - ie running up to today.
Contrast this with :
(1b) Over the last five weeks, Joe has been earning $5000.
(2b) Over the last six months, May has been writing ten essays.
Here we have present tense again, suggesting the time period runs up to today, but perfect progressive aspect - suggesting that the event has been on-going and may continue. Here the meaning would be :
(1b) Over the last five weeks, Joe has been earning $5000 a week.
(2b) Over the last six months, May has been working on ten essays simultaneously.
So it's not a matter of "which is correct?" but of which verb form expresses the meaning that the speaker wants to convey.