To find the distance between the points \((0,0)\) and \((3,4)\), 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, the coordinates are:
- \((x_1, y_1) = (0, 0)\)
- \((x_2, y_2) = (3, 4)\)
Substituting the coordinates into the formula gives:
\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2} \]
This simplifies to:
\[ d = \sqrt{3^2 + 4^2} \] \[ d = \sqrt{9 + 16} \] \[ d = \sqrt{25} \] \[ d = 5 \]
Therefore, the distance between the points \((0,0)\) and \((3,4)\) is \( \boxed{5} \).