While it seems somewhat awkward, this is what can be done to achieve the goal:
SELECT FLOOR(10000 + RAND() * 89999) AS random_number
FROM table
WHERE random_number NOT IN (SELECT unique_id FROM table)
LIMIT 1
Simply put, it generates N random numbers, where N is the count of table rows, filters out those already present in the table, and limits the remaining set to one.
It could be somewhat slow on large tables. To speed things up, you could create a view from these unique ids, and use it instead of nested select statement.
EDIT: removed quotes
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