How does the heat energy from the sun cook an egg within 5 minutes?

The energy of insolation (the rate energy is delivered from the sun) is approximately 1350 watts/square meter, of which about 1000 watts per square meter reaches the ground.

If you think about it, that means a square meter of ground, on a full sunny day, receives about as much solar energy as is put out by a 1000 watt microwave oven on full power.

Is it any wonder at all that some contrivance could be made to concentrate the energy enough to cook an egg, which is fully cooked at about 180°F (82°C)?

You haven't described your egg cooking method or device, so I cannot comment further on how it works, but really, there is little left to add that is not a question of physics or practical engineering.

Wikipedia's solar cooker article shows many methods of cooking with direct solar energy if you are curious.

I'm going to assume that you used a solar reflector or a solar oven.

The sun (as with any star) gives off a lot of energy, but it decreases with distance, as the total radiation is spread across a sphere of increasing size. The Earth's orbit being eliptical means that we're between 147 Gm (billions of meters, or millions of km) and 152 Gm from the sun. The surface area of a sphere is a function of radius squared, so we're looking at 6.5% stronger sunlight perihelion (in January) than aphelion (in July).

The sun's activity also varies on an 11 year cycle (or 22 year, if you take the polarity of the active regions (aka sun spots) into account), but most total solar irradiance measures normalize to the effective W/m^2 at 1AU (149.6 Gm). Based on spacecraft observation it's near 1360 W/m^2, but you have to remember that this is from measurements above the atmosphere; not all of it reaches the ground, and there's significant variability based on the angle of the sun (if it's directly overhead or at a lower angle where there's more atmosphere between you and the sun) and your height above sea level.

And then there's problems with clouds, contrails, volcano plumes, smoke, or other dimming. There are some ground-based measures of solar irradiance, but I don't typically deal with that community. NREL should have maps on their website, but I can't confirm, as I'm having trouble connecting right now.

So the problem is ... what took 5 min to cook today, even using the same gear, might take a different amount of time the next time you try it.

We can offset this variability by concentrating the amount of sunlight into a smaller area. Similar to using a magnifying glass to start a fire, we just concentrate the amount of light into a smaller area to increase the amount of power acting on the item we're trying to cook.

The easiest solar cooker is just a simple set of reflectors; it's similar to a satellite dish, where you collect sunlight over a larger area and focus it into a small spot. (although, we don't want too small of a spot for cooking, or you'll just end up burning one spot).

You can make your own solar cooker with some large pieces of cardboard or other stiff material, something shiny (mylar or aluminum foil) to cover them, and a piece of food to concentrate the heat on (a broken egg in a dish is typical; you can also try a hot dog or marshmallow on a stick).

For faster cooking, we also attempt to limit how much heat escapes from the cooker -- you typically see these called 'solar ovens'. You make a greenhouse from a closed box (possibly insulated and painted black on the inside to absorb sunlight) with a glass lid, and panels around the side to reflect sun into the box. It takes a little bit of effort to cook a full meal, as the longer times mean that you have to adjust it as the sun moves through the sky.

(disclaimer : I've never done solar cooking other than the little experimental demonstrations ... but in college I was on a solar car team (sunrayce & world solar rallye), and I currently do IT support for a solar data center)