Tom Hanks has hinted that #5 is a possibility.
Also, there's this:
Does "Toy Story 4" mark the end? We sure hope not. Five reasons why we expect to see Woody, Buzz and the gang in a fifth movie. (Spoilers ahead!)
That article was nothing but click bait. There was zero substance.
From a story perspective, Woody's story seems done. TS3 was the end of the Andy era of his life. He and the gang started a new with Bonnie, but Woody kind of lost his role as leader over the years. So, he basically retired. I cant imagine a story where it makes sense for him to come back.
All the previous movies left open the door for a sequel. Even TS3, which seemed like a fitting end. But TS3 was also the start of a new life with Bonnie. TS4 has Woody as a free toy. He is separated from the other characters.
A TS5 would either leave out the gang that stayed with Bonnie and focus on Woody and the lost toys, or focus on Bonnie's toys without Woody, which makes little sense since it was always Woodys story. After TS3 a sequel was unnecessary, but now it seems unlikely.