How can the code be modified to ensure that the minutes increase by five, even when the hour changes?

The issue can be solved by checking if the minutes have reached 60 and incrementing the hour by 1 while resetting the minutes to 0. This way, the minutes will always increase by five, even when the hour changes. 

$hour = 1;
$minutes = 55;

// Increment minutes by 5
$minutes += 5;

// Check if minutes have reached 60
if ($minutes >= 60) {
    $hour += 1;
    $minutes = 0;
}

echo "Hour: $hour, Minutes: $minutes";

Keywords

PHP date time modification increment interval

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