When can I start with regular exercising at the gym?

Resuming exercise too soon after liposuciton can increase swelling (edma) and possibly even cause small areas of bleeding that produce firm hard bumpy areas. To minimize this exercise should be avoided for 3 weeks 

Now that it has been five weeks after your liposuction, you can probably return to your preoperative exercise regimen, slowly, and with your surgeon's approval. I doubt there would be any harm at this time if you were to resume an aggressive exercise program.