The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Use UNION ALL instead of UNION (query line: 45): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `journaltransactions` ADD INDEX `journaltransaction_idx_accountid` (`AccountID`);

The optimized query:

SELECT
        journaltransactions.ID,
        journaltransactions.isDebit,
        journaltransactions.AccountID,
        SUM(Amount) AS Amount 
    FROM
        journaltransactions 
    WHERE
        journaltransactions.AccountID <> 78 
        AND journaltransactions.date BETWEEN '2018-11-29' AND '2018-11-29' 
    UNION
    SELECT
        journaltransactions.ID,
        journaltransactions.isDebit,
        journaltransactions.AccountID,
        SUM(Amount) AS Amount 
    FROM
        journaltransactions 
    WHERE
        journaltransactions.AccountID <> 795 
        AND journaltransactions.date BETWEEN '2018-11-29' AND '2018-11-29' 
    UNION
    SELECT
        journaltransactions.ID,
        journaltransactions.isDebit,
        journaltransactions.AccountID,
        SUM(Amount) AS Amount 
    FROM
        journaltransactions 
    WHERE
        journaltransactions.AccountID <> 56 
        AND journaltransactions.date BETWEEN '2018-11-29' AND '2018-11-29' 
    UNION
    SELECT
        journaltransactions.ID,
        journaltransactions.isDebit,
        journaltransactions.AccountID,
        SUM(Amount) AS Amount 
    FROM
        journaltransactions 
    WHERE
        journaltransactions.AccountID <> 89 
        AND journaltransactions.date BETWEEN '2018-11-29' AND '2018-11-29' 
    UNION
    SELECT
        journaltransactions.ID,
        journaltransactions.isDebit,
        journaltransactions.AccountID,
        SUM(Amount) AS Amount 
    FROM
        journaltransactions 
    WHERE
        journaltransactions.AccountID <> 90 
        AND journaltransactions.date BETWEEN '2018-11-29' AND '2018-11-29'