There's no single general answer to your question.
Changing the aperture from f/2.8 to f/2 won't narrow the Depth of Field (DoF) as much as changing the aperture from f/2.8 to f/1.4 will.
Changing the shooting distance from 15 feet to 10 feet won't change the DoF as much as changing the shooting distance from 15 feet to 5 feet.
And changing it from 10 feet to 5 feet will change it a lot more in terms of ratio but less in terms of absolute linear DoF than from 15 feet to 10 feet.
Also, the difference in perspective between shooting at 18mm from 4.9 feet and at 55mm from 15mm will be far more noticeable than any difference in DoF.
In your case what it seems you really want to know is which will minimize DoF the most: shooting at 18mm and f/3.5 or at 55mm and f/5? It still depends on the shooting distance you need with each focal length to get the framing you want.
The following examples assume standard viewing conditions: an 8x10 print viewed at 10 inches by a person with 20/20 vision. Change any of those variables and the DOF for the exact same image will change.
If you want framing that requires 15 feet at 55mm, using f/5 will give you 4.62 feet of DoF: 2.0 feet in front of the point of focus and 2.62 feet behind it.
To get the same framing at 18mm, you'll need to shoot from only 4.9 feet. At 18mm and f/3.5 that distance will give you 3.31 feet of DoF: 1.15 feet in front of the focus distance and 2.16 feet behind the point of focus.
As you can see, the total DoF is shallower at 18mm and f/3.5 from 4.9 feet than at 55mm and f/5 from 15 feet. What may be less obvious is that the DoF is more evenly distributed both in front of and in back of the focus distance with 55mm-f/5-15' than at 18mm-f/3.5-4.9'.
Now let's look at the same focal lengths and apertures, but shot from the same 10 foot distance. Of course this means the same objects will be 1/3 as large in the 18mm shots as in the 55mm shots.
55mm-f/5-10' gives 2.01' DoF: 0.91 in front of and 1.1 behind the 10' focus distance.
18mm-f/3.5-10' gives 24' DoF: 4' in front and 20' behind!
At 10 feet shooting distance the DoF is 12x as deep at 18mm-f/3.5 as at 55mm-f/5! And while the DoF is almost evenly divided in front of and behind the point of focus with the 55mm focal length, it is five times deeper behind than in front of the focus distance with the 18mm focal length.
A funny thing happens if we shoot both focal lengths from 5 feet.
55mm-f/5-5' gives 0.49' DoF: 0.23" in front and 0.26' behind the 5' focus distance.
18mm-f/3.5-5' gives 3.72' DoF: 1.24' in front and 2.48' behind the 5' focus distance.
At 5 feet shooting distance the DoF is only about 7.6x as deep at 18mm-f/3.5 as at 55mm-f/5! And while the 55m focal length distributes the DoF almost evenly between front and back, the 18mm focal length still gives twice as much of the DoF behind the focus distance as in front of it.
One final example. Let's shoot from 100 feet with 55mm-f/5 and from 33 feet with 18mm-f/3.5 to frame our very large subject the same.
55mm-f/5-100' gives infinite DoF: 50.3' in front of the 100' focus distance and all the way to infinity behind the focus distance. So everything further than 49.7' from the camera will fall within the DoF!
18mm-f/3.5-33' gives infinite DoF: 22.7' in front of the 33' focus distance and all the way to infinity behind the 33' focus distance. So everything further than 10.3' from the camera will fall into the DoF (for standard viewing conditions)!
Even though the DoF field doesn't start until further from the camera when using 55mm-f/5 at 100 feet, there is 50' of DoF in front of the 100 foot focus distance. On the other hand, everything from 10.3'away from the camera is in focus when using 18mm-f/3.5, but that is only 22.7' in front of the 33' subject distance. Which of these two options will appear to have more or less DoF than the other may or may not be the one that actually has more DoF in front of the subject, due to the difference in magnification between the two focal lengths as well as how the elements in the scene other than the focused on subject are arranged!
Hopefully these examples have made it clear that DoF is a fairly complex calculation based on a large number of variables. Not only do the focal length, distance, and aperture affect DoF, but there is also sensor/film size, display size of the image, viewing distance of the image, and even the visual acuity of the observer to be taken into account. That's why everyone is telling you to plug in the numbers yourself into a DoF Calculator. The comparison between two selected focal lengths, apertures, shooting distance and all of the other variables make it impossible to say exactly how much difference in DoF there will be between 18mm at f/3.5 and 55mm at f/5.
Finally, a word about what depth-of-field is and is not:
In a way, depth-of-field is an illusion. There is only one plane of focus. Everything in front of or behind the point of focus is out
of focus to one degree or another. What we call DoF is the area
where things look, to our eyes, like they are in focus. This is
based on the ability of the human eye to resolve certain minute
differences at a particular distance. If the slightly out-of-focus
blur is smaller than our eye's capability to resolve the detail then
it appears to be in focus. When you magnify a portion of an image
by making it larger or moving closer to it you allow your eye to see
details that before were too close together to be seen by your eyes as
separate pieces of the image.
Since things are gradually blurrier the further they are from the point of focus, as you gradually magnify the image the perceived depth
of field gets narrower as the near and far points where your eyes can
resolve fine details moves closer to the focus plane.
Since depth-of-field is dependent upon viewing size and distance as well as the visual acuity of the viewer it is hard for a camera to indicate depth-of-field if it doesn't know what the display size of the photo will be. Any in-camera DoF measurement is going to be based upon an assumption regarding the eventual viewing conditions of the photograph.
Assuming the standard 8x10 viewed at 10 inches by a person with 20/20 vision is probably a little too broad in the current digital environment. But most of the online calculators still assume this standard viewing size and distance. If you expect to view images at a 1:1 pixel size on a computer monitor, the DoF for the same exact image will be much narrower. After all, viewing a 22MP or so image on a monitor with 96ppi pitch is like viewing a part of a 60x40 inch print!
