Is there any way to get rid of a seroma besides draining?

Most seromas do resolve with repeated needle aspiration, but some do not.  Another option would be to insert a drain like a Seromacath into the seroma for a week or so to allow it to stay flat and hopefully seal up.  If this doesn't work, an irritant called a sclerosant can be injected into the seroma space, the aim of which is to irritate the lining of the open area and promote scar closure.  In the most stubborn of cases, a return trip to the operating room is warranted to remove the chronic seroma lining and directly close the open space.  Hopefully your seroma will resolve without these more aggressive steps, but your surgeon should be willing to support you through the process.

My protocol for seromas are as follows 
Allow at least 2 weeks of adequate drainage of the area 
If the drainage is less than 20 cc in a twenty four hour period then remove one drain (I usually have 2) 
If there is a persistent seroma after the last drain is removed, consider injecting a steroid, betadine or a scerosant 
If the seroma persists excise (or re excise) 
My experience with seromas are that they have to be drained.  This is provided that there is actual fluid present.  You may be able to get an ultrasound and have it drained under ultrasound guidance.  I think at your early stage it is very important to verify that fluid is present
Hope this helps
Dr. Dillon

It does sound as though your plastic surgeon is taking the appropriate steps to resolve your seroma.At 5 weeks there is any increasing possibility that a seroma cavity will form.  If that does occur eventual excision of the cavity may be required.  Please discuss this with your plastic surgeon.