How can I adjust the amount of space between the x-axis and the edge of the plot window? My x-axis labels are oriented vertically and they are running off of the edge of the win
As Paul said, you are using figures. You can get a reference to the current figure with gcf() and then set the spacing as per the FAQ. I've added two lines to your code:
import matplotlib.pyplot as plt
x=[1,2,3,4,5]
y=[1,2,3,4,5]
plt.plot(x,y)
plt.xticks(rotation='vertical')
fig = plt.gcf()
fig.subplots_adjust(bottom=0.2)
plt.show()