"I have arrived home."
Translation:Dotarłam do domu.
"dotrzeć" may have an additional feel of someone waiting for info whether you managed to reach the destination. Like when a girl texts you "tak, dotarłam" after a date because you asked her to text you, so you will be sure that she got there safely. "Przybyłam", as a simple "I arrived", would somehow feel strange in such a context.