** Mods/Sigil devs: as always ... please feel free to remove the thread/links if deemed inappropriate for any reason. **
No guarantee these will work on your hardware, but I've had good luck with them on Ubuntu 11.10 and higher. Basically, anything with glibc >= 2.13 has a pretty good shot--as long as your hardware is "relatively" recent.
So if you don't want to download the 400Mb Qt5 installer and/or mess around with compiling, these might be for you. If they work.

(actually, these packages are only intended as a stop-gap measure until Qt5 becomes part of official package management systems)
These packages contain the necessary Qt5 libs and a script to launch Sigil. It's nothing fancy and you have no choices on where to install (/usr/local), so it would probably be wise to remove/backup any other version of Sigil before proceeding.
Install with a graphical package manager of your choice or just use:
Code:
sudo dpkg -i filename.deb
from a terminal to install, and
to remove. That's it.
You can launch by typing "sigil" at a terminal or a sigil.desktop file will be created in /usr/local/share/applications that you can create a shortcut to (there should also be an entry for Sigil in the "Office" category of most desktop environments' menu system).
File listings for the packages contents are attached.
(File sizes in file listing are for the 64-bit package)
"Current" version - 0.8.6 - w/Qt5.4.1 (~47-49Mb):
The 64-bit Linux deb package (Sigil-0.8.6-Linux-x86_64.deb):
https://drive.google.com/file/d/0Bwu...ew?usp=sharing
The 32-bit Linux deb package (Sigil-0.8.6-Linux-x86.deb):
https://drive.google.com/file/d/0Bwu...ew?usp=sharing
Older Versions:
--------------------------------------
The 64-bit Linux deb package (Sigil-0.8.5-Linux-x86_64.deb):
https://drive.google.com/file/d/0Bwu...ew?usp=sharing
The 32-bit Linux deb package (Sigil-0.8.4-Linux-x86.deb):
https://drive.google.com/file/d/0Bwu...ew?usp=sharing
The 64-bit Linux deb package (Sigil-0.8.4-Linux-x86_64.deb):
https://drive.google.com/file/d/0Bwu...ew?usp=sharing