Pathetic fallacy is when the weather, the climate, or the elements are used to reflect the mood of the story, or the mood of the characters. In romantic films, for example, there is often rain when the two lovers are separated. This is because the rain reflects the miserable, melancholy mood of the two lovers. In some films, there is often stormy weather when something frightening, dramatic, or chaotic is happening. The stormy weather reflects the chaotic, frightening mood of the story.
There are no obvious examples of pathetic fallacy in act 1, scene 5, but this scene does follow directly on from act 1, scene 4, where the weather is described several times. We can assume that the weather in act 1, scene 5, is much the same as it is in act 1, scene 4, and this weather would be demonstrated on stage throughout both scenes. In act 1 scene 4, the weather is described as "very cold." Hamlet says that the "air bites," and Horatio says that the air is "nipping." These descriptions of the climate reflect the mood at this point in the play. The climate is uncomfortably cold, and inhospitable, and reflects that something is, as Marcellus states at the end of act 1, scene 4, "rotten in the state of Denmark."
In act 1, scene 5, Horatio exclaims, "Heaven secure him!" This is not an example of pathetic fallacy because there is no description of the weather, the climate or the elements. Horatio is here simply asking heaven, and by implication the angels or God, to protect Hamlet, who at this point in the play is in a state of extreme emotional agitation. Hamlet has of course just been told by the ghost of his dead father that he was murdered by his own brother, Hamlet's uncle, who is now the king.