Firstly, I know that there are plenty of questions here like this one but hopefully this is not a duplicate.
I was born and grown up in Iran and belong to a religious minority (Bahai faith). As you know Bahais are not allowed to attend universities in Iran because of their faith. I was no exception and so could not study at university because of my religious beliefs. Between the age of 18 (when I finished my highschool in Iran) and 24, I worked as a construction laborer. At the age of 24, I together with my family (my parents and sister) travelled to Turkey and became refugees in UNHCR and two years later UNHCR sent us to Australia. I studied English for two years and after that I repeated year 11 and 12 because Australian universities did not accept my Iranian qualifications. At age 30, I started my undergraduate studies in Bachelor of Electrical Engineering and I will graduate very soon. I am now 35 years of age and would like to apply to be a PhD student in the first 5 or 10 top engineering schools in the world. I have maintained a GPA of 6.9, a WAM of 93 and was on Dean's merit list every year except the first year of my undergraduate studies. There is a possibility that I also get university medal but that is not certain yet.
Should I explain these details to the graduate admission committee explaining why I started my undergraduate studies very late at the age of 30? and what I was doing before that?