a+b=5-c
(a+b)c+ab=3
(5-c)c+ab=3
ab=3+c^2-5c
a+b=5-c
a,b为方程x^2-(5-c)x+c^2-5c+3=0两根
△=(5-c)^2-4c^2+20c-12>=0
即-1<=c<=13/3
故最大值为13/3