I was raised on the British school system that taught that there were 5 Continents:- Europe, Africa, North America, South America and Asia. Now that I live in North America I keep hearing that there are 7 Continents. Which one is correct? both? 5? 7? Any thoughts? How is this subject being teached in other parts of the world?

If I remember correctly, Antartica and Australia were added to your 5 to make up our 7.

when?

Am I that old?

If that's what you were taught, Partyon, I'll hand the British school system a "fail" grade. The answer is seven. Even though we're used to being ignored, I find it difficult to believe that the system would have omitted Australia, and in addition there's Antarctica. Both are big enough and geographically isolated enough to qualify as continents. The list is thus Europe, Africa, Asia, Australia, North America, South America and Antarctica. I think it's reasonable to separate the two Americas for this purpose.

And I hope the British school system didn't teach you that the past tense of the verb "to teach" is "teached", either

Funny how this topic keeps rearing its head.
The answer to your question is: there's no 'correct' answer.
Depends on where you are doing your schooling, but some geographers/educators feel there are 5 continents, some 6, some 7.
Reasons:

-some people view Eurasia as one.
-some people view the Americas (N & S) as one.
There is no universally agreed upon answer because the definition of continent is not rigid enough.

and why does everyone leave Greenland off this list and call it an island?

Now Gilligan had an island.

I too grew up in England and was taught that there were five continents, but that included Australia. For some reason North America and South America were combined into one. This was in the 1970s. Now I live in the U.S. and my kids are taught that there are seven, which seems to me to be correct. Lighten up, Neil.

Sorry, it's a.m. here, and in addition to being a grumpy old man all day I'm not a morning person. It's worse when there's a full moon.

I used to wonder about Greenland until someone explained the Mercator projection.

My recollection is that Antartica was not considered a continent until it was learned that there is a land mass there. In other words its not just ice. I could be all wet on this one.

Well, I honestly hadn't ever heard of a 4 continent world, but apparently some people consider Africa/Europe/Asia to be one continent as well "Eurafrasia".
Here's a summary from "word IQ":

There is no single standard for what defines a continent, and therefore various cultures and sciences have different lists of what are considered to be continents. In general, a continent must be large in area, consist of non-submerged land, and have <geologically significant borders>. While some consider that there are as few as four or five continents, the most commonly used counts are six or seven.

Two of the largest disagreements in listing continents are whether Europe and Asia should be considered separately or combined into Eurasia, and whether North America and South America should be considered separately or combined into America. A few geographers have also suggested grouping Europe, Asia, and Africa into a continent of Eurafrasia (see Africa-Eurasia).

The seven continent model is commonly taught in Western Europe and North America, while the six continent (combined Eurasia) model is also taught in North America and is the primary continent model used in scientific contexts. The six continent (combined Americas) model is commonly taught in Eastern Europe and South America.