diff --git a/chapter05/chapter05.xml b/chapter05/chapter05.xml
index 8a05daca5..1a2393b93 100644
--- a/chapter05/chapter05.xml
+++ b/chapter05/chapter05.xml
@@ -9,7 +9,7 @@
   <?dbhtml dir="chapter05"?>
   <?dbhtml filename="chapter05.html"?>
 
-  <title>Cross Compiling a Toolchain</title>
+  <title>Compiling a Cross-Toolchain</title>
 
   <xi:include xmlns:xi="http://www.w3.org/2001/XInclude" href="introduction.xml"/>
   <xi:include xmlns:xi="http://www.w3.org/2001/XInclude" href="toolchaintechnotes.xml"/>
diff --git a/chapter05/introduction.xml b/chapter05/introduction.xml
index 5614270b2..28b496993 100644
--- a/chapter05/introduction.xml
+++ b/chapter05/introduction.xml
@@ -10,20 +10,15 @@
 
   <title>Introduction</title>
 
-  <para>This chapter shows how to build a minimal Linux system.
-  This system will contain just enough tools to start constructing the final
-  LFS system in <xref linkend="chapter-building-system"/> and allow a working
-  environment with more user convenience than a minimum environment would.</para>
+  <para>This chapter shows how to build a cross-compiler and its associated
+  tools. Although here cross-compilation is faked, the principles are
+  the same as for a real cross-toolchain, and are detailed in the next
+  section.</para>
+
+  <para>The programs compiled in this chapter will be installed under the
+  <filename class="directory">$LFS/tools</filename> directory to keep them
+  separate from the files installed in the following chapters. The libraries,
+  on the other hand, are installed into their final place, since they pertain
+  to the system we want to build.</para>
 
-  <para>There are two steps in building this minimal system. The first step
-  is to build a new and host-independent toolchain (compiler, assembler,
-  linker, libraries, and a few useful utilities).  The second step uses this
-  toolchain to build the other essential tools.</para>
-<!--
-  <para>The files compiled in this chapter will be installed under the
-  <filename class="directory">$LFS</filename> directory to keep them
-  separate from the files installed in the next chapter and the host
-  production directories. Since the packages compiled here are temporary,
-  we do not want them to pollute the soon-to-be LFS system.</para>
--->
 </sect1>