Assuming that the marbles are equally distributed in the bag, let's first determine the probability of drawing a green marble.
Since there are 5 colors of marbles (red, yellow, green, blue, and white), the probability \( P \) of drawing a green marble is:
\[ P(\text{green}) = \frac{1}{5} \]
Mr. Lim will conduct 50 trials. To find the expected number of green marbles he will pick, we can use the formula for expected value, which is:
\[ \text{Expected number of green marbles} = P(\text{green}) \times \text{Number of trials} \]
Substituting the values:
\[ \text{Expected number of green marbles} = \frac{1}{5} \times 50 = 10 \]
Thus, Mr. Lim can expect to pick \(\boxed{10}\) green marbles.