Who's afraid of Russian Nouns...? [me!]
You see, Hanna, cases of English pronouns are not very simple either. If you had given the full answer to this question, you would have said: "I'm afraid of Russian nouns", and short answer is "Me", so a subject form was replaced by an object one without any reason.
or do you think it's possible?
It is possible, of course. If you hear one hundred times "два рубля", but "пять рублей", it will become natural for you. But first you need to study the rule. Then you will (and you do it now) hear the confirmation of this rule every day.
I can give you one more exaple from English.
I can give it to you.
In the two sentences above the presense of the preposition "to" depends on whether the direct object is a noun or a pronoun, the word order changes too. ("I can give you it" is ungrammatical). In Russian in both cases "мне" will be used with many possible word orders.
Can it be mastered by listening and reading? Was it overwhelming for you?