probability – how to solve the poisson distribution problem? totally feeling lost

For part(a), I tried to use Pr(X=4)=Pr(X=5)to calculate and having this
((e^(-µ))(µ^4))/4!=((e^(-µ))(µ^5))/5!but I don’t know how to continue solving for the µ. And for the remaining, I cannot even think of the way of solving them.
The number of cracks in a section of highway that is significant enough to require repair is assumed to follow a Poisson distribution. Let 𝑋 be the number
of cracks in 10km, and we have the information that the probability of 4 cracks in 10km is
equal to the probability of 5 cracks in 10km (Pr(𝑋 = 4) = Pr(𝑋 = 5))
(a) Please find the Expect value 𝑋 (The expect cracks in 10km) and the
Variance of 𝑋.
(b) Find the number of cracks in 10km which have the largest probability.
(c) What’s the probability that at least one crack requires repair in 4km of the
(d) Let 𝑌 be the number of cracks in 4km, sketch the (CDF) Cumulative
Distribution Function and graph up to 𝑦 = 4.5.
(e) If we should order the material to fix the cracks beforehand, how many
packages of the material (One package for one crack) shall we order to ensure that all
the cracks in 4km can be fixed with at least 95% chance?