5w represents a winter viscosity index generally measured at 0'C(in cSt) while the w40 represents the viscosity at 100'C!
The grades:
0w-40
5w-40
10w-40
15w-40
20w-40
will all have the SAME viscosity at 100'C or as you say Higher temperatures but will have different viscosity at lower temperatures, to be more specific at 0'C!
Likewise all the following grades(If some grades don't exist, just consider them as example):
15w-20
15w-30
15w-40
15w-50
will all have DIFFERENT viscosity at 100'c but same at 0'C

Look at the following link, the viscosity in centiStokes at different temperatures hope even further add up to your knowledge:
ISO Grade Oil Properties



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