Adding Time to their clock?

You are mistaken. You each get 5 seconds added for every move. Your game went 45 moves before you lost on time. 45 moves would have added almost 4 minutes to the 5 you started with. Your opponent probably did a lot of thinking while it was your move and only used 4 minutes during the game.

You can check the times now.  While some of his moves used only 0.1 seconds because of premoves, your opponent never got more than 5 seconds added to his remaining time.

Look at this position. You had plenty of time (1:14) and an easy win. 

You missed the idea of Rxc7+ and axb5 and then the game would be all but over. Instead, you used all your time.

It is hard to lose such positions. I think I know how you feel. I often lose on time. Sometimes it seems like time just disappears. I constantly need to work on playing more quickly. That is all there is to do.

Wow.  I had no idea.  That's embarrassing.  So a person can do pre-moves?  Thank you so much for helping me out.  I guess it just goes to show how little I know about the game.  Thank you again!

When it says 5I5 it means 5 seconds are added every move...if it is 5I15 seconds, and so on...

I was playing a 10|0 rapid with over a 1.5 minutes and my opponent  less than 10 seconds. What happened next is a mystery! Besides the fact that I lost I dont think this is a good way to play as this was a tournament and I was not made privy of this rule. I stopped moving after he did it about 4 times coz I dont think I would do that in a game.

That sucked. I feel robbed of a good game

No time gets added after moves in 10 0 games.

I’ve played the last several games and I have position and pieces when  both times start blinking... when the blinking stops,  I loss time or I loss because the game claims it was abandon!!! What the heck man! I think I’m being cheated

Blinking clocks is an indication of a disconnect from the live server process.

https://support.chess.com/article/213-how-do-i-fix-my-disconnect-lag-issues

The number on left is your total time. The number on the right is additional seconds per move. 

10|0 means 10 minutes, +0 sec per move

5|5 means 5 minutes, +5 sec per move.

10|15 ....and so on

I didn't notice my opponent "gaining time" throughout the game, until it got to the last ten or so seconds on their clock. I had over a minute of time left, so I thought I would win by time out. I noticed every time he made a move, time would get added to the clock. Was he just pre-moving all his pieces in the last ten seconds? Guy was being a sheet talking douch who would've lost under normal time restraints to what he derided as my "nooby", "mentally retarded" self.

Your last game was a 5|2 game which means 2 seconds are added to each player's clock after their respective moves.

For those and any non-increment games, lag compensation and/or disconnects can also be a factor.

https://support.chess.com/article/423-why-did-the-clock-times-suddenly-change-the-clocks-seem-broken