storing datetime modifications + formats

Question

I have a requirement where the user wants to be able to save "Date Modifier" strings to a database, and then use that with other dates in their application.

e.g. -

id   name              date_modifier
1    Add 1 Year        +1 year
2    Last Day Of Month last day of this month

// simplified; using DateTime
echo $date->modify($date_modifier);
// today = 02/03/2022
// Add 1 Year = 02/03/2023
// Last day of month = 31/03/2023

Essentially I'm passing a date modifier string to a DateTime object to modify it.

This seems to be working OK but I am running into issues -

For example; some of the requirements are 5th of {whatever date is supplied} this isn't working / I don't know what a date modifier looks like to achieve this.

$date = '02/03/2022';
$date->modify($fifth_of_month);
// outputs 05/03/2022

My next thought was to also store date_format so I wouldn't modify this date; but I would format it as $date->format('Y-m-05')

Is there a better approach to this as this looks like it could get very messy very quickly?