A rope of length 10 [i]m[/i] is tied tautly from the top of a flagpole to the ground 6 [i]m[/i] away from the base of the pole. An ant crawls up the rope and its shadow moves at a rate of 30 [i]cm/min[/i]. How many meters above the ground is the ant after 5 minutes? (This takes place on the summer solstice on the Tropic of Cancer so that the sun is directly overhead.)
1. **Determine the distance traveled by the ant's shadow:**
   - The ant's shadow moves at a rate of 30 cm/min.
   - After 5 minutes, the distance traveled by the shadow is:
     \[
     30 \, \text{cm/min} \times 5 \, \text{min} = 150 \, \text{cm} = 1.5 \, \text{m}
     \]

2. **Set up the problem using similar triangles:**
   - The rope forms a right triangle with the flagpole and the ground.
   - The length of the rope is 10 m, the distance from the base of the flagpole to the point where the rope touches the ground is 6 m.
   - By the Pythagorean theorem, the height of the flagpole is:
     \[
     \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8 \, \text{m}
     \]
   - The triangles formed by the ant's position on the rope and its shadow are similar to the original triangle.

3. **Set up the proportion using similar triangles:**
   - The side ratio of the similar triangles is given by the ratio of the shadow's distance to the base of the original triangle:
     \[
     \frac{1.5 \, \text{m}}{6 \, \text{m}} = \frac{x}{8 \, \text{m}}
     \]
   - Solving for \( x \):
     \[
     \frac{1.5}{6} = \frac{x}{8}
     \]
     \[
     \frac{1.5}{6} = \frac{1}{4} = \frac{x}{8}
     \]
     \[
     4x = 8
     \]
     \[
     x = 2
     \]

4. **Conclusion:**
   - The height of the ant above the ground after 5 minutes is 2 meters.

The final answer is \( \boxed{2} \, \text{meters} \)