Solution:
Given the expression below
[tex](x+5)^8[/tex]Applying the binomial theorem formula
[tex]\begin{gathered} \left(a+b\right)^n=\sum_{k=0}^n{\binom{n}{k}}a^{n-k}b^k \\ Where \\ a=x \\ b=5 \\ n=8 \\ k=4\text{ i.e. fifth term} \end{gathered}[/tex]For the fifth term, i.e
[tex]\sum_{k=4}^8{\binom{8}{4}}x^{8-4}5^4=\frac{8!}{4!(8-4)!}\cdot x^4\cdot(625)=(70)(625)(x^4)=43750x^4[/tex]Hence, the fifth terms is
[tex]43750x^4[/tex]