It is from a much older version of Russian. I think, it was still Г in Old East Slavic and in Church Slavonic. In high style the pronunciation ого/его was still OK in the 18th century.
And Г did not alwasys mean a velar stop: in the southern dialects the sound changed into a voiced velar fricative ɣ (which is why Harry Potter is Гарри Поттер; some foreign names have a legacy transliteration inherited from times when it still made sense).
If any of you guys can forward me to an article about this (in any language) I would be ever so gr8tful. I could find no explanation, some Russian Friends of mine told me they were told not to ask anymore when inquiring about this in school.
Hell, why didn't I think about this before? 10 lingots to whomever posts the first link.
Check this one, too
Apparently, В instead of Г was used from about XV - XVI century onwards.
This book has it, too. Look at the chapter about the history of the pronouns and scroll down a bit (initially, Old East Slavic only had 1st and 2nd person pronouns).
Here is an article of some relevance (although certainly not what you are looking for - no need for lingots ;-) ), which describes the differences between the Church Slavonic language (which would be the Slavic analogue of Biblical Hebrew) and modern languages: https://en.wikipedia.org/wiki/Church_Slavonic_language
Check the last entry for Standard Russian.
Btw, a lingot for your correct use of "whomever", it is something Duolingo can't wrap it's head around (or extract it from a certain orifice).
A more-or-less literal translation would be "Мне это нужно на пять недель". Note that we do not use "that" in this position that often, so IRL you would replace it with он/она/оно depending on what "that" is and rephrase things a bit.
НА + Accusative is used for some "temporary" time spans, when something is/was/will be valid for some time but then will return to "as usual".
- Я уеду на неделю. → means that you'll leave and are going to be away for a week.
- Не кладите бананы в холодильник более, чем на день или два. ~ Do not put bananas into the fridge for more than a day or two.
- Она задержалась на шесть месяцев. ~ She had a six month long delay (i.e. something delayed her doing something for 6 months)
- Мы сняли квартиру на полтора месяца. = We rented an apartment for a month and a half.
Note that usually the verb you use expresses the action that puts things in this state—the state that will hold for the amount of time specified. For example if you want the window to stay open for 10 minutes, you ask someone to "open it for 10 minutes".
Нужно/надо do not quite fit the scheme but still work. If you mean a phrase someone might say to borrow something for a while, a more common way would be to ask for a permission to "take" something for 5 weeks. Stating that you need something for some time is possible but I cannot easily think of a context where you'd have to use that.
If you said "нужны", nobody would blink, but a native would most likely use "нужно": five weeks here are treated as a single quantity, a measure of a single time span. It's hard for me to explain this coherently, but if you said "нужны", that would "break" that time period into its constituent parts.
I think this is not dissimilar to how many English speakers would say "Five apples costs (not cost!) two dollars" - they would treat them as a single unit. Curiously, this actually sounds wrong to me (not a native English speaker), and I would use "cost". Perhaps "нужно/нужны" is a similar thing.