Lag = Time that takes the communication between client and server to go from one to another.

Freeze = When your hardware or software halt for some time and lower the overall performance.

So, the lag you have don't have anything to do with your fps, your fps are directly caused by your hardware and software.

For what you said it seems that you have a resident program that every 5min do something "heavy" and make the pc freeze. What you should do is to open the game and leave the task manager windows also open and check which process is making the cpu go to 100%

Onces you find it post it here.