I've got a 5th grade math question. How can finding the product of 5 x 700 help you check the product of 5 x 789?

You know the product 5*789 must be more than the product 5*700.
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We sometimes compute 5*789 as
  5*(700 + 80 + 9) = 5*700 + 5*80 + 5*9 = 3500+400+45 = 3945.
In this case, computing 5*700 is an essential part of finding the product.

Sometimes, we compute 5*789 as
  10*789/2 = 7890/2 = 3945
Realizing that the answer must be larger than 5*700=3500 can serve as a check that the math was done properly.