When did Sarah Jane move to 13 Bannerman Road? She hasn't always been living there, as I remember seeing her living somewhere else in The Five Doctors.
Sometime between 1983 and 1999.
We don’t have an exact date, but we can make a reasonable guess.
In The Wedding of Sarah Jane Smith, Clyde says:
“But Sarah Jane's loaded, right. All this money from her aunt. The house…”
which tells us that she inherited the house from her aunt, probably on her death. Her aunt was Lavinia Smith, who has a pretty reasonable history in the canon. But her death isn’t recorded in a TV episode, so we have to go into the supplementary books and comics.
The comic City of Devils is set in 1983, and starts with Lavinia inviting Sarah Jane to Egypt to investigate a newly discovered city. If she’s still alive, then she probably hasn’t given the house to Sarah Jane yet. (This is the same year that The Five Doctors aired, so if you assume that the real-world matches up with Sarah Jane’s timeline, then it’s consistent with her not living there, as noted in your question.)
Then there’s the novel Millenium Shock, set in 1999 as we’re all grappling with the Y2K bug. We see Sarah Jane sorting through her aunt’s things, and another confirmation that she was bequeathed the house:
She stood up. “I have to get back to Moreton Harwood, sort out Aunt Lavinia’s things. And there’s the house too. Keep the pen for me, Harry. It’s one less thing to worry about.”