You are experiencing is a defect that appear on DLP TV equivalent to the "dead pixel effect for LCD.

The DMD (Digital Mirco-mirror Device) chip started to have some stuck element. In such a position those always reflect the light, so they appear are always lit pixel. You probably also have some stuck on the opposite position making dark pixel, but those are lot less apparent.

This is a major defect and is fixed at no cost if you still are under the 1 year warranty:
http://www.samsung.com/us/support/repairpolicy/servicePolicyWarrantySearch.do?group=&type=&subtype=&model_nm=HL-T5675S&dType=D&mType=UM&vType=R&prd_ia_cd=02010300&acc_ia_fl=&disp_nm=HL-T5675S&menu=repairpolicy

If you are no more covered by this or any extended warranty, the TV will need a new light engine block (very few repair shop only change the DMD chip as it's very integrated and would require lot of labor).

It is Never going to get better on your own. It will get much worse.

Samsung have a service locator here:
http://www.samsung.com/us/support/repairlocation/serviceLocator.do?group=&type=&subtype=&model_nm=HL-T5675S&dType=D&mType=UM&vType=R&prd_ia_cd=02010300&acc_ia_fl=&disp_nm=HL-T5675S&menu=repairlocation
Any TV repair shop that services DLP based TV should be able to perform that fix.