What is the temp. of the ground, 5 ft deep, 50 ft deep. 500 feet deep?

The rate of change of temperature with depth is referred to as the geothermal gradient. The geothermal gradient varies depending on location, so there is no uniform answer. On average, the geothermal gradient is approximately 75 degrees F per mile. In volcanically active areas, the gradient can be as high as 150 degrees F per mile. In ocean trenches, the gradient may be as low as 15 degrees F per mile. Decay of naturally occurring radioactive elements may also cause localized increases in temperature in some locations.

That depends on several variables to get an accurate esitmate.

1) What is the water content?

2) Where on earth are you looking (geographic location)?

3) What is the organic/radioactice content of the soil?

4) What is the ambient air temp?

5) What time of day/year is it?

All those play a large fator in how the soil temperature profile would look. Without that info you cannot clearly answer this question. Remember a winter soil temperature profile will look vastly different than a summer soil temperature profile.

Tentoes is right. for example, the temperature of the ground at the South Pole at all of those depths will be different than the same depths in Death Valley, Ca.

You get the idea. Also, there is not a formula for determining it. In other words, we can't say 'take the surface temp., and subtract 5 degrees for every foot down you go.' . This is because different soils insulate at different rates. The sand of a desert will not carry the heat of the sun at the same rate as granite or ice. I wish there was a magic answer, but unfortunately, it is different in every location.

What is the surface temperature? This information is needed first before the question can be answered.