Will upping my string gauge be fine?

I've been thinking about replacing my strings and getting some slightly thicker strings cause my band downtunes to drop C# and it can get a little bit floppy down there. I was only thinking of going from a set of Ernie ball regular slinky (50, 70, 85, 105) to a set of power slinky (55, 75, 90, 110) but I'm worried that even that tiny increase might mess with the nut. Is that change something that would still fit with my stock nut or would I have to file it down for that?

Would also want to know if there would be any problem playing in normal E standard with those strings.