What is the main external conflict in this story ?

The main external conflict in "Contents of the Dead Man's Pocket" is involved in the problem of retrieving a sheet of yellow paper that has blown out the window. At first it seems like a relatively simple matter, even though the scene is set eleven floors above the street. The paper is only about five yards from Tom Benecke's apartment window. The ledge is about as wide as the length of his shoe. The weather is clement, which explains why he opened the window in the first place. But when Tom gets out on the ledge and sidles a short distance towards the paper, he realizes that he has more logistical problems than he had anticipated. He can only proceed by facing the wall and holding onto the bricks with his fingertips. And when he does get to the precious paper, he finds that he can't bend over to pick it up without risking losing his balance and falling to his death.
Up to that point his internal problems have been relatively minor. He had decided that he would just not look down. That way the height would not be a serious factor. But when he is finally forced to look down in order to pick up the yellow sheet of paper, he gets a full, horrible view of Manhattan at night from eleven stories up.

...he lowered his right shoulder and his fingers had the paper by a corner, pulling it loose. At the same instant he saw, between his legs and far below, Lexington Avenue stretched out for miles ahead.
He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. 

After this the story changes from an external conflict to an internal conflict. Tom has to start moving back towards his apartment window in spite of his nearly overpowering terror and the sense of vertigo which seems to be pulling him backward off the narrow ledge and out into empty space.