This is a very common problem for learners of all languages (and I've even seen some native-speaker English teachers make big mistakes with this in English lessons!).
We like to talk about things being countable, but really it is nouns that are countable (even when the noun may be both countable and uncountable).
The word money gives us the idea of general money. When we think about this idea, we don't think about numbers. This is the same way that we don't think about numbers when we think about water.
When we think about water, we can think about the amount of water we have. We think about litres (or pints or gallons). Now, we don't usually have a million waters, but we can very easily have a million litres of water. The same thing happens with money. We don't usually have a million moneys. But we can have a million pounds, or a million yen or a million dollars.
This may seem strange when you think about it. An easy way to understand it though is to think about your own language. What is the word for money in your language? Can you say: 5 money in your language? You can't!
What is the currency in your country in your language (dollars, yen, roubles, lira etc)? Can you say "5 (X)" —5 dollars, 5 yen, 5 roubles, 5 lira, 5 (currency)s— in your language?
Yes you can!
It works the same way in English too!