If utensils (spoons, spatulas, etc.) aren't counted, my five basics would be:

1. One large, deep, skillet with a cover.

With one of these one can cook almost anything. Such a skillet can be used to fry, sautee, or even boil a good amount of pasta, rice, or noodles. It can be used for browning meat, if one eats meat. Skillet dinners, of course, require one of these.

2. One small skillet (if it needs to be covered the large cover could be used)

As with the larger skillet, a small skillet can be used to cook almost anything - only less of it. I use mine for boiling small amounts of pasta, as well as for single-serve stir fry, sandwich melts, sauteed vegetables, and, of course, eggs.

3. One large pizza pan

While it's nice to have a collection of baking sheets, rectangular baking sheets won't work for pizza. On the other hand, one large pizza pan will come in handy for pizza, heat-and-bake frozen pies, and most things requiring a cookie sheet.

4. One loaf pan (8.5 x 4.5)

A loaf pan this size will, as its name implies, serve for baking meatloaf or breads/cakes that require a loaf pan. I use mine for cranberry, nut, banana, pumpkin, and other similar "breads" (that are really more like cake).

5. A strainer of some sort (a collander is good, but a hand-held strainer can be even handier)

Ideally, having both a collander and hand-held, pan-strainer is best. Given the choice of only one, however, I'd choose a hand-held because sometimes it's easier to just tip up that over-sized skillet (or "proper" pan), and strain the water without dumping the contents of the pan. While a colander comes in handy for washing vegetables, if only five cooking items are allowed, doing without the less-handy collander wouldn't be too difficult; since vegetables could be washed in the over-sized skillet (if necessary) and strained with the hand strainer.

A collander is "just one more big thing" to wash and is not as versatile as a hand-held strainer, which is why I choose the hand-held.

If utensils are counted among the five items then I would do without the loaf pan and pizza pan, and include, instead:

One large spoon that would not scratch non-stick cookware

One large spatula that would not scratch non-stick cookware

There is a whole lot of basic cooking that could be done with the above items. If a large mixing bowl, a glass measuring cup, and a set of measuring spoons could be added, one would have quite a few cooking possibilities.

If I had to choose only three basic cooking items, and utensils counted, I would choose the small skillet, the large spoon, and the spatula. With just those all kinds of things can be cooked. (There are always plates and alumuninum foil that can be used as makeshift covers. Plates, of course, should not be used when the burner is on.)