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Refactor for Testability

HardCoding00:00
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Your question is Refactor for Testability. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

Noir Consulting's internal delivery team relies on a small Java utility to close out consultant timesheets at the end of each billing cycle. The class below computes the invoice amount, applies the standard discount, and writes a confirmation, but nobody on the team has ever been able to unit test it: every attempt ends up needing a live database and the real system clock.

public class TimesheetProcessor {
    static List<String> AUDIT_LOG = new ArrayList<>();

    public double closeTimesheet(String consultantId, double hoursWorked) throws SQLException {
        DatabaseConnection db = new DatabaseConnection("jdbc:postgresql://prod-db:5432/billing");
        double rate = db.getRateForConsultant(consultantId);

        double total = hoursWorked * rate;
        if (hoursWorked > 40) {
            total = total * 0.85;
        }

        LocalDate closeDate = LocalDate.now();
        AUDIT_LOG.add(consultantId + " closed on " + closeDate);

        db.writeInvoice(consultantId, total);
        System.out.println("Invoice for " + consultantId + ": " + total);

        EmailService.send(consultantId + "@noirconsulting.com", "Your timesheet has been closed.");

        return total;
    }
}

Explain, in plain text, everything about this class that makes it resistant to unit testing, and what you would change so it could be tested without a live database, a real clock, or a real mailbox.