Getting primary custody of a child is very subjective. It will depend on what county your case is in and who the judge is. You can present your case and reasons why custody should change but that does not always guarantee that the judge will see it like you do. Please understand that in Texas, the judge is required to determine what is in the "best interest of the child." Since the child is only 5 years old, the child will not have a say in this matter. The judge will have to base his/her decision on the facts that you and the ex-wife present. Thus, your job is to bring out all the reasons why the child will suffer by remaining in her mother's care for a majority of the time. You will need to be prepared to show how your residence and living situation will be beneficial to the child. If the grandparents are brought in as witnesses to show that she leaves the child with them frequently and you can show that the same would not happen with you, then that would be in your favor.
Unfortunately, I cannot give you a straight answer but understand that a carefully crafted case goes a long way when trying to change primary custody of a child.
I am not certain how you personally define "primary" custody, but I am guessing that you mean you would like to be the parent whom the child lives with on a day to day basis. Whether or not you can change primary custody depends on many factors. The most important will be whether or not your request to change custody is in the best interests of your daughter. "Best interests" is not clearly defined by statute and will vary from case to case. Another factor to consider is how long it has been since you and your ex-wife entered into the parenting agreement you have now, and whether or not there has been a significant change in circumstance to warrant an early revision if it has been less than 3 years. The Courts are most interested in the safety and welfare of your child, so if you believe that the current arrangement is potentially dangerous to your child's mental or physical health, you are always entitled to ask for the court's assistance so as to avoid any harm.
Good luck to you and your daughter. If you have any further questions or would like to discuss your case in greater detail, feel free to contact me. My contact information is available on Avvo and also through the website link below.