I’m 5’3 and weigh 135. Is 800cc Possible? Could I have my dream boobs? (photos)

At 5'3" and only 135, 800 cc implants will be too heavy and large for your frame and tissue. Please do not choose implants that are too big. Large and heavy implants carry higher risks and will sag over time. I would suggest meeting with a board certified plastic surgeon, being examined and measured, and trying on sizes that best fits your frame and tissue.

Thank you for the question and pictures.  Based on your photographs, I think that you are starting at a good place and should have a very nice outcome with breast augmentation surgery.    I also think that your goal photographs are realistic, understanding of course that goal photographs are communication tools not guarantees of exact outcome.It is not necessarily that larger implants are more problematic;  it is that the use of a breast implant  that is TOO  large for a patient's frame can be problematic.  
Generally speaking, every patient undergoing breast augmentation surgery should understand that their anatomic starting point will limit the outcome of breast augmentation surgery.    In other words, a patient's starting anatomy will limit how large of a breast implant can be utilized safely. The use of a larger breast implant (than what is safely "allowed" by the patient's anatomy) can be problematic;  potential problems include breast implant displacement/malpostion issues ( such as bottoming out, lateral displacement, symmastia...)  and/or significant breast implant rippling/palpability.
 
  Generally speaking, the best online advice I can give to ladies who are considering breast augmentation surgery (regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully. Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. ***Ask to see lots of examples of his/her work. Sometimes, it is necessary to seek several consultations before you feel comfortable about your choice.
2. Have a full discussion and communication regarding your desired goals with your plastic surgeon. This communication will be critical in determining breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as “natural” or "D or DD or DDD cup” etc may mean different things to different people and therefore prove unhelpful.
Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup size may also be inaccurate. Again, best not to discuss your goals and/or judge the outcome of the procedure performed based on achieving a specific cup size. The use of computer imaging may be very helpful during the communication process. The use of in bra sizers may also be helpful. In other words, use as many “visual aids” as possible during the communication process. I encourage patients to meet with me as my times as necessary, to feel comfortable that we are both on the “same page”.
3. Once you feel you have communicated your goals clearly, allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals. Again, in my practice, this decision is usually made during surgery. I generally select appropriate breast implant size/profile after the use of temporary intraoperative sizers and viewing the patient's chest in the upright and supine positions.
 
I hope this helps. Best wishes for an outcome that you will be very pleased with.