"Tell" here means "know or be certain". The writer is saying that, considering his grandmother's age, he could not be certain that he would see her when he returned after five years, because she might die during that time. The final words "but my grandmother could" imply that his grandmother had no such uncertainty, and in the following paragraph the writer says: "After five years I came back home and was met by her at the station". The writer is, perhaps, subtly conveying the arrogance of youth, because the young man ignores the fact that he himself could not be sure of being alive in five years' time.
Tell (Cambridge Dictionary)
The Portrait of a Lady by Kushwant Singh