Ratio is a way to compare two quantities by expressing their relationship in terms of division. In this case, we need to find the ratio of 5 meters to 10 kilometers.

1. Understanding the Conversion:
To find the ratio, we need to express the quantities in the same unit. Let's convert the units so that both are either in meters or kilometers.

1 kilometer (km) is equal to 1000 meters (m). Therefore, 10 kilometers can be written as 10,000 meters.

2. Expressing the Ratio:
Now that both quantities are in meters, we can express the ratio. The ratio of 5 meters to 10,000 meters can be written as 5:10,000.

3. Simplifying the Ratio:
To simplify the ratio, we can divide both quantities by their greatest common factor. In this case, the greatest common factor of 5 and 10,000 is 5.

Dividing 5 by 5 gives us 1, and dividing 10,000 by 5 gives us 2,000. Therefore, the simplified ratio is 1:2,000.

4. Comparing the Ratio to the Options:
Now, we can compare the simplified ratio to the options given.

a) 10:1 - This ratio does not match the simplified ratio of 1:2,000.

b) 2000:1 - This ratio does not match the simplified ratio of 1:2,000.

c) 1:2000 - This ratio matches the simplified ratio of 1:2,000.

d) 1:10 - This ratio does not match the simplified ratio of 1:2,000.

Therefore, the correct answer is option C. The ratio of 5 meters to 10 kilometers is 1:2,000.