Let the number of red marbles be r, the number of green marbles be g, and the number of white marbles be w.

From the given information, we have the following relationships:

1. $w = r - 3$ (3 fewer white marbles than red ones)
2. $w = g + 5$ (5 more white marbles than green ones)
3. $w = 10$ (there are 10 white marbles)

Now, solve for r and g.

From $w = r - 3$: $10 = r - 3$ $r = 13$

From $w = g + 5$: $10 = g + 5$ $g = 5$

The total number of marbles is: Total marbles = $r + g + w = 13 + 5 + 10 = 28$