Non-alternating margins in book class

Why don't you just change from twoside to oneside? The following example works for me just fine.

\documentclass[oneside]{book}

\usepackage[margin=1cm, bindingoffset=5cm]{geometry}

\usepackage{lipsum} % serving demonstration purposes only

\begin{document}
\lipsum[1-25]
\end{document}

The default value is twoside, and when you have a twosided document left and right margin specification will transform into inner and outer.

You should change the margin values of course.

When in twoside mode, geometry uses left as inner and right as outer. You can use bindingoffset for this:

\usepackage[
  top=1.25in,
  bottom=1.25in,
  left=1.25in,
  right=1.25in,
  bindingoffset=0.25in,
  heightrounded,
]{geometry}

With the last option you get an integer number of lines for the text height, the rounding is as small as possible, usually unnoticeable.

This wouldn't be my preferred page setup, to be honest.

I solved this with the following technique:

First, \usepackage{layout} in the preamble and then \layout in the body to see what was happening.

Then,

\usepackage[top=1.25in, bottom=1.25in,
            left=1.5in, right=1.25in, twosided]{geometry}
\setlength{\oddsidemargin}{36pt}
\setlength{\evensidemargin}{36pt}

For book class, this ignores alternating pages (all pages are identical), and all margins are 1.25 in, except the left which is 1.5 in.