A 5' rise and an 8' run is not so long that you need to divide it with a landing. You can easily enough just run it directly. It is actually a benefit to have a longer run, so each step can be a bit wider and more shallow. Easier to climb and more space for each step which is a benefit to people like me with size 12 shoes.
You really don't want your stair to go 5' rise for 5' run as this translates to a fairly steep 45 degree angle. You don't NEED it to be that steep, so don't make it that way.
Be prepared. Building deck stairs is like the PhD of deck construction. When you think you've got everything measured and just right. Measure it all a second time. Don't assume that the end of your deck is actually plumb or level. Check it to be sure. I just got finished building a new stair off the back of my deck and it was a royal pain.
Oh, and overbuild the stair with reinforcements, and metal hangers at both ends. The stair takes more strain than pretty much any other part of the deck.
Best of luck. And keep us posted as to how it turns out.