To find the distance between the points \( N(0, 4) \) and \( O(5, 4) \), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, we have:
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (5, 4) \)
Substituting these coordinates into the formula gives:
\[ d = \sqrt{(5 - 0)^2 + (4 - 4)^2} \]
Calculating inside the square root:
\[ d = \sqrt{(5)^2 + (0)^2} = \sqrt{25 + 0} = \sqrt{25} = 5 \]
Thus, the distance between point \( N \) and point \( O \) is \( \boxed{5} \) units.