I love mine and I'm about the same height as you.

Most I use are in the 8" range.... but... really hard to dedicate room under the kitchen sink for bins. Plumbing traps & disposals take priority.

Love my 10" sink!

Also 5’7”. Have a 10” sink. Works well for me. We have a disposal and also room for trash/recycle..... Not much room for anything else though.

I'm 5'7" (or used to be), and I don't find my 10" single-bowl sink to
be too deep if I'm rinsing something, or loading the DW. If I hand wash
more than a few items, I put a cooling rack in the bottom, and set a
large bowl on it for the wash water, so that I don't need to reach so
far into the sink.

I hacked a standard sink base to accept the
deeper sink, and re-used shorter doors from a demolished cabinet. My
19.5" tall Rev-a-shelf trash bin might have just fit, except for the
fact that I reinforced the front of the cabinet with a 2x4 because I was
paranoid about a 33" sink full of water being too heavy for the re-used
cabinet. In reality, I rarely have the sink filled with water, and then
it's only partly filled if I'm washing or chilling scalded produce.

The
19.5" height of the pull-out includes the plastic bin and the slider,
so it's 19.5" from the cabinet floor. I have a center back drain, so I'm
assuming you'd have an off-set drain.

Check the specs on your
trash pull-out and measure the amount of space available in the sink
cabinet, taking drain and garbage disposal locations into consideration.
Even if there isn't quite 19.5" (or whatever your trash pull-out
height), don't despair. I think you could cut the bottom two inches off
the plastic bins and set the top part that remains over the sliced off bottoms.
Then use trash can liners as usual. The sliced off bottom 'trays' would
catch any leaks from the bottoms of the bags.

I have this relatively inexpensive pull-out, which I installed about 8 years ago, and have had no issues with it:

30 quart pull-out (door brackets sold separately)

I use the single bin for trash. Recyclables are kept in the mudroom.