Need a 5 page paper

Your plan needs a bit of revision in order to establish a shared theme the stories explore and some their details more accurately.

Summing up the theme of the stories as "determination" oversimplifies both stories and seem a inaccurate portrayal of the themes that "To Build a Fire" explores.  

Phoenix is certainly determined--and her determination helps her to complete her journey successfully--which is getting medicine for the grandson--not finding him as you've stated.  However, to get at the themes of this story--you need to go beyond her determination--to her motives for that determination--her love for the grandson and her willingness to sacrifice her comfort for his benefit.

Yes, the man was determined--but his determination did not save him--if anything it doomed him.  The man failed to complete his journey and died because of his arrogance.  He had been warned not to travel alone when it reaches a certain temperature--but he ignored this advice because he thought he was capable of taking care of himself.  By the end of the story, he realizes that he was foolish to disregard the advice--his arrogance has been replaced with humility.

To connect the stories thematically, you really need to recognize the symbolic significance of each story's journey.  If not viewed symbolically--there isn't really any significant similarities between the stories.  Phoenix is not in a life and death struggle with the natural environment the way that the man is.  Her journey would be a relatively easy walk through the Mississippi countryside to town--if it were not for her age and her deteriorating mind.

However, if the journeys depicted in each story are view as symbols of our "journey" through life--we can see connections that exist. 

In both journeys--just as in our lives--the characters must face both expected and unexpected obstacles.  Both characters have prepared themselves for the expected obstacles--and are able to overcome them.

However, the man was not able to overcome all of the unexpected obstacles--and died.  The story identifies his lack of imagination--his inability to consider the significance of things--particularly his insignificance, his frailty, his mortality, his need of companionship.  The story emphasizes that he was in need of a trail mate.  The man was doomed because of his ignorance and arrogance--which was finally replaced with experience, wisdom, and humility--but too late to save him.

Phoenix, on the other hand, seems to have the traits the man was missing--experience, wisdom, humility--and she is able to overcome the unexpected obstacles--even the loss of her memory--because of these traits.  Her love for her grandson sustains her even when she no longer remembers that love precisely--because it has become an ingrained part of her.  This love and connection to others--provides her with the trail mate that the man lacks.

These are some ideas to consider as you continue to plan your essay.  Feel free to contact me if you have questions.