Sensor cleaning is offered at most camera stores and repair facilities but at high costs. In today's age of mirrorless cameras, sensor cleanings seem to be needed more frequently. You should not be afraid to clean your own sensor.
This method of cleaning applies to mirrored cameras as well. You just have to take a few extra steps to lock the camera up. Refer to your camera's manual for "Cleaning mode". When I shot with a 5D I still cleaned my own sensor, however it was less often.
The key, like proper lens cleaning, get the big dust that will scratch off first by using a blower or vacuum brush. This is the kit that I use by Delkin.
First you use the sensor scope to look at your sensor in order to get an idea of how much dust is present. Use your blower to remove as much as you can.
Next you will wet the sensor cleaning brush with sensor cleaning solution. Apply to the bottom half of the brush and only on one side of the brush if you have a double ended brush.
To clean, angle the brush at about 45 degrees and you do long slow continuous sweeps across the sensor. The motion should be pulling the brush across the surface of the sensor. Be gentle however it is ok to apply some pressure.
After you have used the wet side of the sensor brush, look through your sensor scope to see if you missed any dust. If you did miss any dust then use the opposite end of the sensor brush or the dry end and push the dust off doing the opposite motion of pulling the brush across the surface of the sensor. If the dust is persistent then repeat from the beginning with a new brush.
The reason most people are afraid to do this is because if you scratch your sensor it is a very expensive repair. If you are uncomfortable then perhaps its worth paying the price of this kit every time you need a cleaning. Personally I am faced with a dirty sensor too often to have to rely on someone else doing it and the cost would be atstronimical.