#### Answer

The tank holds approximately 499 gallons.

#### Work Step by Step

After adding one gallon containing radioactive material, everything was mixed.
The gallon that was removed contained $\frac{10}{5000} = \frac{1}{500}$ of the original radioactive particles. If each of the other 499 gallons remaining in the tank has the same amount of radioactive particles, that would account for all of them.