Just recently I have noticed that emails downloaded on my Galaxy S5 are being deleted from my server so I cannot view them on my laptop. How do I change this?
The most probable answer is that you have your tablet configured to use POP3 for email instead of using IMAP. You can check this in the account section of your email app.
Using POP3 to retrieve your emails deletes them from the server whenever they are downloaded to your tablet. Using IMAP synchronizes your email app with the server, so that the emails are in both places.
If this is correct, the simplest solution is to delete your your email account from the app and then set it up again correctly, using IMAP instead of POP3. Your email app may be able to simply edit the settings of the account to use IMAP instead: however, depending on what app you are using, this may be the equivalent of deleting an account and adding a different one, I.E., you might still lose your already-downloaded emails.
Please note that you should back up all your emails on the tablet first, as this solution may delete them from the tablet. (And, since you are apparently using POP3, they will already be missing from the server.)