Unfortunately I will not offer very good technical advise on this, but read on.

> 
> The fun part is that horde_webmail needs to have php5.6 for almost all of
> its packages.
>

I just looked here to make sure I get the picture:
https://www.horde.org/apps/webmail/docs/INSTALL
Under prerequisites it says "PHP 5.3.0 or above" and frankly I cannot see how
a newer version of PHP would be the source of any serious problems. I could
certainly be wrong, but I am suggesting to dismiss that as a potential problem.
 
> Is there any way to install BOTH php 5.6 and php7.0 without them
> conflicting?
>

I'd say throu all the installation in a VM that has an older OS installed, say
an OS that says has PHP 5.8 packaged in it. Make sure it works out of that VM
before you trying doing things that can lead to more problems that you cannot
quickly solve.


Given that this is probably in support of your business, I'll give you this
piece of "business development" advise: get your mail service working by
having a company like Google handle it for free via Gmail first. You can sort
out your own mailserver and web-mail items later. In fact, you can have your
own mail-server and allow gmail to be the front-end service (via IMAP), which
is what users see when they are using email. Horde can be something that you
can trouble-shoot later. The idea is that you will, very quickly, get going
so that you can focus on the business side first and leave technical details
for the time that details can be sorted out. An added benefit is that you do
not have to worry about maintaining the reputation of a mail-server if you
allow Gmail to handle it all. You will find that you will have to work a bit
harder to keep your server off blacklists. I do know that we all prefer to
keep the "evil empire" off our e-mailboxes...