From the problem we see that d+e>c+d leading to e>c and b+c>a+b leading to c>a so we have a<c<e so far b+c>c+d so b>d and e+a<d+e so d>a leading to A is the lowest as b,c,d,e are greater as we also know the highest plus lowest is the middle so e+a is highest +lowest leading to E is greatest and A is lowest

if 2 of the expressions being compared share a number, the other numbers of those 2 expressions can be compared so then $a+b<e+a => b<e$ $a+b<b+c => a<c$ $c+d<d+e => c<e$ $e+a<d+e => a<d$ $c+d<b+c => d<b$ so we have $a<d<b<e$ and $a<c<e$ therefore $a$ is the smallest and $e$ is the largest

$a+b<e+a\implies b<e\quad(1)$ $a+b<b+c\implies a<c\quad(2)$ $c+d<b+c\implies d<b\quad(3)$ $c+d<d+e\implies c<e\quad(4)$ $e+a<d+e\implies a<d\quad(5)$ $(1),(3),(5)\implies a<d<b<e$ $\implies \max(a,b,c,d,e) = e; \min(a,b,c,d,e) = a$