Conditional formatting with two IF criteria

I've read through a bunch of this forum's postings and googled, but cannot find an answer, so some help would be greatly appreciated.

Here's the situation: I'm a teacher and I need to determine whether my students meet the requirements to go on an internship abroad. Some requirements are simple, such as having completed all the course work from the first year. I can do this quite easily and it works. However, should a student wish to do the internship in a language other than English, he needs to meet more detailed requirements:
If the student is currently at level 3 in this language, he needs to complete this level with at least a 7.
If the student is currently at level 5 in this language, he needs to just pass this level, which is a 5.5.

I have two columns, one for level and one for score. What I'd like to do is change the color of the score cell green if the student meets the requirements and red if he doesn't. I've tried this in a number of ways, with regular conditional formatting, with some IF formulas, but I can't get it to work. It's probably fairly easy for the more experienced Excel users out there, but it totally baffles me.

Thanks a million!

Yes, of course, sorry.

As you can see, I already worked out the requirements for the first year (prop): the cell turns green when the student reaches 60 credits. For English they need a passing score, so the cell turns green when it's 5.5 or higher and red if below.

Students must choose two of three other languages offered (French, German or Spanish) which is why I have three language columns. But once I get it working for one of them, I can make it happen for the other ones.

Thanks so much for you quick replies.

se1429, I found your post while googling for the answer, but wasn't able to derive it from that. I have put in the formulas as suggested, but nothing happens. The score cell remains white. I attached the new version. I must have made a mistake somewhere but I don't see it.

se1429, I put these in, changed to G2 and H2 obviously, but nothing happens. Cell remains white.

I tried again, but it still doesn't work. I honestly don't know what's wrong.

For the other cells I had to put in the condition regarding empty cells because otherwise it would turn all empty ones red.

Yes, it works! I don't know why it wouldn't before, but it's fixed. Thank you all very much! And now I should know how to do such a thing myself in future.