A chord is 5 cm from the center of a circle with a diameter of 26 cm. What is the length of the chord?

The diameter is given as $26 \text{ cm}$. The radius is half of the diameter.

$$r = \frac{\text{diameter}}{2} = \frac{26 \text{ cm}}{2} = 13 \text{ cm}$$

Let $d$ be the distance from the center to the chord, $r$ be the radius, and $\frac{L}{2}$ be half the length of the chord.
We have a right-angled triangle where the hypotenuse is the radius ($r$), one leg is the distance from the center to the chord ($d$), and the other leg is half the chord length ($\frac{L}{2}$).
The Pythagorean theorem states:

$$r^2 = d^2 + \left(\frac{L}{2}\right)^2$$

Given $d = 5 \text{ cm}$ and $r = 13 \text{ cm}$.

$$(13 \text{ cm})^2 = (5 \text{ cm})^2 + \left(\frac{L}{2}\right)^2$$ $$169 \text{ cm}^2 = 25 \text{ cm}^2 + \left(\frac{L}{2}\right)^2$$

$$\left(\frac{L}{2}\right)^2 = 169 \text{ cm}^2 - 25 \text{ cm}^2$$ $$\left(\frac{L}{2}\right)^2 = 144 \text{ cm}^2$$ $$\frac{L}{2} = \sqrt{144 \text{ cm}^2}$$ $$\frac{L}{2} = 12 \text{ cm}$$

The full length of the chord is twice half its length.

$$L = 2 \times 12 \text{ cm}$$ $$L = 24 \text{ cm}$$

The length of the chord is $24 \text{ cm}$.