If Mr. Lim has an equal number of marbles of each color and there are five colors (red, yellow, green, blue, and white), then the probability of drawing a green marble in one trial is \( \frac{1}{5} \).
In 50 trials, the expected number of green marbles he would pick can be calculated as follows:
\[ \text{Expected number of green marbles} = \text{Number of trials} \times \text{Probability of picking a green marble} = 50 \times \frac{1}{5} = 10. \]
Therefore, Mr. Lim will expect to pick \( \boxed{10} \) green marbles.