Males with 5-ARD do not have a uterus or other female internal structures, but they do have what looks like a vagina, so are often sexed as females. However they are males with normal testes, which produce typical male hormones. Those hormones, among other things, prevent the development of female internal reproductive structures (like the uterus and cervix).
In embryonic development, we all start out with two sets of primordial duct systems, one set that will develop into the male internal reproductive stuff (the Wolffian ducts, which become the epididymis, vas deferens and seminal vesicles), and another that develops into the female internal stuff (the Müllerian ducts, which become the upper part of the vagina, cervix, uterus and fallopian tubes, pic at the end).
In males, fetal testes don't only produce testosterone! They also make Anti-Mullerian Hormone (AMH), which is crucial for getting rid of the Mullerian ducts, and thus, ensuring that the eventual uterus, etc. don't develop. If there's no testes and no AMH, that female internal stuff will develop.
Males need high levels of T for male-typical development of all the male reproductive structures. Without T production and action, the external (penis and scrotum) and internal (described above) genitalia won't develop. But as I wrote in my monster tweet yesterday, T alone isn't enough for development of the penis and scrotum (and prostate): for that, T must be converted into DHT (a more potent androgen, production pathway below), and people with 5-ARD don't make the necessary enzyme to carry out that conversion. So they end up with what appears to be a vagina.
FYI, some males inherit a genetic mutation that means they can't produce AMH. They are typical males, but have a nonfunctional uterus and fallopian tubes inside their abdomen. The condition often not discovered until adulthood (it's called Persistent Müllerian Duct Syndrome). AMH is an important hormone for males, but hardly anyone even knows it exists.
Also, the testes generally don't descend into the scrotum before birth (as usual) without DHT, but they often do at puberty when testosterone levels reach high concentrations. So males with 5-ARD may be "sexed" as female, due to the female-appearing external genitalia.
But brain and the rest of the body are typically male. Most people with the condition will "transition" to living as a male once they realize they are male, and this often happens at puberty, when the testes descend and the body develops in a typically masculine way.