You can pull a common factor from both terms:
[tex]5^{31}-5^{29}=5^{29+2}-5^{29}=5^{29}(5^2-1)=24\cdot5^{29}[/tex]
Next, pull a factor of 4 from 24, and 25 from the power of 5; since 100 = 25*4, we have
[tex]5^{31}-5^{29}=\underbrace{5^{27}\cdot6}\cdot100[/tex]
