1. **State the problem:** We need to find the value of $\cos \theta$ for a right triangle where the adjacent side to angle $\theta$ is 5 and the hypotenuse is $\sqrt{29}$. 2. **Recall the formula for cosine:** $$\cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ 3. **Substitute the given values:** $$\cos \theta = \frac{5}{\sqrt{29}}$$ 4. **Rationalize the denominator:** Multiply numerator and denominator by $\sqrt{29}$ to eliminate the square root in the denominator. $$\cos \theta = \frac{5}{\sqrt{29}} \times \frac{\sqrt{29}}{\sqrt{29}} = \frac{5\sqrt{29}}{29}$$ 5. **Interpretation:** The cosine of angle $\theta$ is $\frac{5\sqrt{29}}{29}$. 6. **Match with options:** This corresponds to option D. **Final answer:** $\boxed{\frac{5\sqrt{29}}{29}}$ (Option D)