You'll need to go up in height by five in order for the tire size to remain the same.
I.e. 265/65/18 is the same size as a 265/70/17.
If you stick with the same actual size, no extra trimming.
Nope, that's backwards. A 285/70/17 is the same size (relatively, might be off by a tenth or two) as a 285/65/18. For each size the rim goes up, the aspect ratio decreases.
This site is a great tool for figuring out different sizes, very helpful.