Simplify. Assume \( d \) is greater than or equal to zero. \( 5 \sqrt{12 d^{3}} \)

To simplify \( 5 \sqrt{12 d^{3}} \), we start by breaking it down. First, we can simplify the square root component: \[ \sqrt{12 d^{3}} = \sqrt{12} \cdot \sqrt{d^{3}}. \] Next, we calculate \( \sqrt{12} \), which can be expressed as \( \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \). Now, simplify \( \sqrt{d^{3}} \). We can write \( d^{3} = d^{2} \cdot d \), so \[ \sqrt{d^{3}} = \sqrt{d^{2} \cdot d} = \sqrt{d^{2}} \cdot \sqrt{d} = d \sqrt{d}. \] Putting it all together, we have: \[ \sqrt{12 d^{3}} = 2\sqrt{3} \cdot d \sqrt{d} = 2d\sqrt{3d}. \] Finally, multiplying this by the 5 we started with gives: \[ 5 \sqrt{12 d^{3}} = 5 \cdot 2d \sqrt{3d} = 10d \sqrt{3d}. \] Thus, the simplified expression is: \[ \boxed{10d \sqrt{3d}}. \]