Chapter 5 of this novel is titled "Three Broken Threads". The threads in this case refer to to threads of the case - three different possible leads that could further the investigation. The leads are centered around Sir Henry and who is following him. Holmes meets Sir Henry at his hotel room to tell him that he [Henry] is beling followed and to try to convince Henry that he should not return to Baskerville Hall at the moment. Henry is emotional and tries to insist that he will and Holmes insists that Watson accompany him.
While this is happening, Holmes sends a telegram to make sure that Barrymore is at Baskerville. He gets a positive response, and so has to eliminate Barrymore as the one following Henry. Holmes also discovers that Henry is due to inherit a million pounds, but if he dies, than a cousin by the name of Desmond gets it.
As the men start out the door, Henry finds his boots that had been missing before, suggesting that someone had removed and then returned them.
In the evening, Holmes gets a telegram confirming that the London Times is also not the one following Henry. The the cab driver that was suspected shows up to defend himself, describing the passenger that requested that Henry be followed and explaining that the passenger introduced himself as Sherlock Holmes. Holmes realizes that this criminal is clever and a worth opponent.