Use universal email, but it won't be fully automated.
1) simply apply universal email to the page when you store the user profile. Also store the date they filled out the form in the database. Have two yes/no fields for Letter2sent and Letter3sent to your database to keep track of when they are sent.
2) Create a page on the web site admin that shows all users who have been in the system for at least 48 hours and don't have the Letter2Sent field set to yes.
3) Add a button that will send the emails to those people and update the field to set it to 'yes' so that they won't get the email again.
4) create a second page and a second email repeating 2 and 3 from above for the 5 day later scenario.
the end user (your client) will need to log into the website daily to initiate the emails on the corresponding pages. There is no way to automate something with code on a web page days later because the code on the web page won't run until someone visits that page.