Let's analyze the image to solve for $BD$, given that $AB = 5$.

Key observations:

• $\triangle ABD$ is the main triangle.
• $\angle A = 60^\circ$, and since $AB = 5$, we can use trigonometry to solve for other sides.
• There is a right-angled triangle $\triangle BCF$, where $\angle C$ is $90^\circ$.
• $AB = BF$, and $AD = BD$ (since these segments are marked as equal).

Solution strategy:

1. Since $AB = 5$ and the triangle is isosceles with $AB = BF$, the triangle's symmetry can simplify the process.
2. Use trigonometric functions, like cosine or sine of $60^\circ$, to relate the sides $AB$, $AD$, and $BD$.

I'll now solve for $BD$.The length of $BD$ is approximately $10$ units.

Would you like more details on the steps, or do you have any additional questions?

Here are five related questions for further practice:

1. How would you find the length of $AD$ in this triangle?
2. What is the length of $BC$ if $BF$ and $FC$ are known?
3. Can you calculate the area of $\triangle ABD$ based on the given information?
4. How would you use the Pythagorean theorem in $\triangle BCF$ to find side lengths?
5. How does knowing that $AB = BF$ help in solving similar problems?

Tip: In isosceles triangles, symmetry can often simplify calculations. Use this property whenever possible to reduce complex steps.