1. The problem is to evaluate the expression $5^{34}$. 2. The expression $5^{34}$ means multiplying 5 by itself 34 times. 3. This is an example of exponentiation where the base is 5 and the exponent is 34. 4. There is no simpler factorization or simplification for $5^{34}$ other than calculating its value. 5. The value of $5^{34}$ is a very large number: 717897987691852588770249. 6. Therefore, the final answer is $5^{34} = 717897987691852588770249$.