Find the length of DNA sequence?
The mutation rate per haplotype per site is $\mu = 10^{-5}$. Assuming diploidy and a population size of $N=5000$, the population wide mutation rate per site is $10^{-5} * 5000 * 2 = 0.1$. 

$0.1$ is hence the probability that a mutation occurs a at a given site (in the whole population). For 10 sites the probability that a mutation occurs at at least one site is $1 - (1-0.1)^{10} = 0.65$.

The probability we are aiming for is 0.95. So let's write the equation

$$1 - (1-0.1)^{x} = 0.95$$

, where $x$ is the number of sites we are looking for. You just have to solve for $x$ now and round up to the larger integer.