In R2015a, using hold on (and hold off) instead of hold all, the plot displays correctly:
N=[10 100 1000 10000 100000];
lengths=[5e-2 1.6e-2 5e-3 1.6e-3 5e-4];
n=logspace(1,5);
rate=1./sqrt(n);
loglog(N,lengths,'x','LineWidth',2,'Color','k')
hold on
loglog(n,rate,'LineWidth',1,'LineStyle','--','Color','k');
hold off