First, the 500 rule is an idea for low quality lenses, web sized images, or for people who don't car about short star trails. Here is the real story:
Your t5i has 4.3 micron pixels. With an 18 mm lens, the 500 rule is 500/18 (or 500/(18*1.6)) giving 28 or 17 seconds.
Stars on the celestial equator move 15 arc-seconds per time second. The pixel spacing in arc-seconds is:
- plate scale = 206265 * pixel size in mm / focal length in mm
- so plate scale for your camera with an 18-mm lens is:
- plate scale = 206265 * 0.0043 / 18 = 49.3 arc-seconds.
- A star will cross one pixel every 49.3 / 15 = 3.29 seconds.
The 500 rule above (28 or 17 seconds) would give star trailing of 28 / 3.29 = 8.5 pixels or 17 / 3.29 = 5.2 pixels.
A couple of pixel trail will be noticeable with a sharp lens. So a 200 rule is needed for actual round images with good lenses.
The key to astrophotography is collecting light. The f/ratio tells light density, but not total light gathered from the subject. Larger physical aperture diameters collect more light. Recommendations like 11 mm f/2.8 means an aperture diameter of only 3.9 mm, smaller than dark adapted human eyes.
An 18 mm f/1.8 lens (as in the Sigma 18-35 f/1.8 art lens) has an aperture of 10 mm, and collects ( 10 / 3.9 )2 = 6.6 times more light than an 11 mm f/2.8 lens from the subject. A 24 mm f/1.4 lens has an aperture of 17 mm; a 35 mm f/1.4 has an aperture of 25 mm and would collect ( 25 / 3.9 )2 = 41 times more light than an 11 mm f/2.8.
So get the largest aperture diameter lens that fits your subject in your field of view (or do a mosaic). The other way to get more light is longer exposure times. For night sky, that means a tracker. Something like an iOptron Skytracker (about $400) can track lenses 100 mm and shorter for long periods.
I would recommend the Sigma 18-35 f/1.8 Art lens for crop cameras, or Sigma art 24 f/1.4. If you use a tracker and will consider mosaics, the Sigma art 35 f/1.4 is in my opinion the best lens for nightscapes under $1000.
