Although Google can be hit or miss, these phrases all make sense and are something that a native English speaker would say. Here are some alternatives if you are looking for another way to say these ideas.
The day before yesterday... - Two days ago...
Three days ago... - (this is the best way to express this idea)
Five days from now. - ...in five days
The day after tomorrow. - Two days from now...
Hope this helps!
-Weston