If all of your transactions are in the same tax year there is zero difference in outcome.
Basic accounting with no wash sale yields a net $1 gain:
Transaction 1 Transaction 2
Buy $10 Buy $4
Sell $5 Sell $10
Result -$5 Result +$6
Net +$1
Now consider wash sale, with a disallowed and appropriate cost basis adjustment you get the same $1 gain.
Buy $10 -> Sell $5 = -$5
Buy $4 within 30 days, adjust cost basis to $9
Sell $10
Net +$1
The ONLY way this would matter to you is if Day 2 is December 31, 2018 and Day 3 is January 1, 2019 because that would mean you could not take the $5 loss in your 2018 taxes.
Your broker probably handles these adjustments as they come up, I believe they have to as part of their requirement to issue appropriate 1099s. Wash sales largely don't matter, particularly if you're opening and closing positions as in your example.
One caveat. These accounting rules apply to all of your holdings, and the holdings of your spouse where applicable, regardless of where they are stored. So, IF you have your assets in multiple accounts, you would have to track this on your own.