According to the problem we start with 6000 gal of E10 which means there is 10% of ethanol in this 6000, with ths information we can calculate the amount of ethanol already in the mixture:
The relationship between ethanol and total fluid can be represented like this:
Based on this relationship we can build the one that we are looking for:
the total solution will be:
where X is the E5 solution volume
and the TotalEthanol would be:
where E5ethanol (5% Ethanol 95% Gasoline) would be:
Now replacing in the relationship we found before:
Solving for X:
We should mix 1500 gal of E5 to make an E9 mixture