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The simplified form of $5\sqrt{18}$ is $15\sqrt{2}$.

To simplify $5\sqrt{18}$, we first need to simplify the square root of $18$. The number $18$ can be factorized into its prime factors:

This allows us to express the square root of $18$ as:

Utilizing the property of square roots, which states that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can separate this into:

Since the square root of a squared number is simply the number itself, we find that:

Thus, we can simplify $\sqrt{18}$ to:

Next, we multiply this simplified form by $5$. Therefore, we can express $5\sqrt{18}$ as:

Multiplying the coefficients outside the square root gives us:

Thus, we conclude that:

In summary, the simplified form of $5\sqrt{18}$ is $15\sqrt{2}$.

This process demonstrates the importance of understanding how to factor numbers and apply properties of square roots—key skills in GCSE Mathematics. By breaking down the problem step-by-step, you can confidently simplify more complex expressions involving square roots.