So I kept trying several things, having no assistance from the hosting company or any response here.
I was able to successfully install 5.6.3.2 using Installatron (which is the process the cpanel on the hosting account uses) separate to my cPanel.
Tried again with 5.7.4.2 but still keep getting the same error.

My host has not found a solution. So I keep trying other things.

I tried installing through MojoMarketplace. I had used SimpleScripts before and that led me to MojoMarketplace.

This error message appeared

"Your server does not meet the necessary requirements for this script:
ERROR: The script requires one of the following: (nginx,apache,iis) and your server is running: litespeed."

Has anyone encountered an error like this before?
I had sent the host the listed requirements including "Concrete5 is run mostly on Apache 2, but will also work on IIS and Nginx" and they said that requirement was met.

Having sent my ISP the Mojo Marketplace error message, I received this reply

"I've changed the PHP version from 5.4 (native) to PHP 5.4 through PHP Selector."

Problem solved.

Loving 5.7.4.2 like I knew I would

@virtivity - Just wondering if you can go into the DashBoard -> System - Settings -> Environment Information and copy / paste the items there, especially the php version installed ...?

I think your host changed it from php 5.4 to php 5.5 .... but the the above will clarify this.

OK..........................

# concrete5 Version
Core Version - 5.7.5.8
Version Installed - 5.7.5.8
Database Version - 20160412000000

# concrete5 Packages
ABC Auto Reply forms (1.0.2), Airstream (.9.4.1), Breadcrumb Trail Page Links (1.1), C5Extras YouTube Channel (2.1.2), Fruitful (1.2), GalleryES (2.5.1), HonestWebsites Simple testimonials (1.0.0), Like This (0.9.1), List files from set (1.0.12), Login/Logout Link (1.0), Palette (1.0.1), QR Code (0.9.1), Simple Slider (1.0), Social Stream (1.2), Spacer (0.9.3), Stucco (1.1.3), Stupid Slider (0.9.1), Under Construction (1.0.1), Vimeo Video (1.0.1), Vivid Carousel (1.0.1), Vivid Store (3.1.4).

# concrete5 Overrides
languages/tr_TR/LC_MESSAGES/messages.mo, languages/tr_TR/LC_MESSAGES, languages/tr_TR, languages/de_DE/LC_MESSAGES/messages.mo, languages/de_DE/LC_MESSAGES, languages/de_DE, languages/nb_NO/LC_MESSAGES/messages.mo, languages/nb_NO/LC_MESSAGES, languages/nb_NO, languages/fr_FR/LC_MESSAGES/messages.mo, languages/fr_FR/LC_MESSAGES, languages/fr_FR, languages/nl_NL/LC_MESSAGES/messages.mo, languages/nl_NL/LC_MESSAGES, languages/nl_NL, languages/da_DK/LC_MESSAGES/messages.mo, languages/da_DK/LC_MESSAGES, languages/da_DK, languages/fi_FI/LC_MESSAGES/messages.mo, languages/fi_FI/LC_MESSAGES, languages/fi_FI, languages/es_PY/LC_MESSAGES/messages.mo, languages/es_PY/LC_MESSAGES, languages/es_PY, languages/ru_RU/LC_MESSAGES/messages.mo, languages/ru_RU/LC_MESSAGES, languages/ru_RU, languages/ja_JP/LC_MESSAGES/messages.mo, languages/ja_JP/LC_MESSAGES, languages/ja_JP, languages/pl_PL/LC_MESSAGES/messages.mo, languages/pl_PL/LC_MESSAGES, languages/pl_PL, languages/it_IT/LC_MESSAGES/messages.mo, languages/it_IT/LC_MESSAGES, languages/it_IT, languages/el_GR/LC_MESSAGES/messages.mo, languages/el_GR/LC_MESSAGES, languages/el_GR, languages/pt_BR/LC_MESSAGES/messages.mo, languages/pt_BR/LC_MESSAGES, languages/pt_BR, languages/sv_SE/LC_MESSAGES/messages.mo, languages/sv_SE/LC_MESSAGES, languages/sv_SE, languages/sl_SI/LC_MESSAGES/messages.mo, languages/sl_SI/LC_MESSAGES, languages/sl_SI, languages/tr_TR/LC_MESSAGES/messages.mo, languages/tr_TR/LC_MESSAGES, languages/tr_TR, languages/de_DE/LC_MESSAGES/messages.mo, languages/de_DE/LC_MESSAGES, languages/de_DE, languages/nb_NO/LC_MESSAGES/messages.mo, languages/nb_NO/LC_MESSAGES, languages/nb_NO, languages/fr_FR/LC_MESSAGES/messages.mo, languages/fr_FR/LC_MESSAGES, languages/fr_FR, languages/nl_NL/LC_MESSAGES/messages.mo, languages/nl_NL/LC_MESSAGES, languages/nl_NL, languages/da_DK/LC_MESSAGES/messages.mo, languages/da_DK/LC_MESSAGES, languages/da_DK, languages/fi_FI/LC_MESSAGES/messages.mo, languages/fi_FI/LC_MESSAGES, languages/fi_FI, languages/es_PY/LC_MESSAGES/messages.mo, languages/es_PY/LC_MESSAGES, languages/es_PY, languages/ru_RU/LC_MESSAGES/messages.mo, languages/ru_RU/LC_MESSAGES, languages/ru_RU, languages/ja_JP/LC_MESSAGES/messages.mo, languages/ja_JP/LC_MESSAGES, languages/ja_JP, languages/pl_PL/LC_MESSAGES/messages.mo, languages/pl_PL/LC_MESSAGES, languages/pl_PL, languages/it_IT/LC_MESSAGES/messages.mo, languages/it_IT/LC_MESSAGES, languages/it_IT, languages/el_GR/LC_MESSAGES/messages.mo, languages/el_GR/LC_MESSAGES, languages/el_GR, languages/pt_BR/LC_MESSAGES/messages.mo, languages/pt_BR/LC_MESSAGES, languages/pt_BR, languages/sv_SE/LC_MESSAGES/messages.mo, languages/sv_SE/LC_MESSAGES, languages/sv_SE, languages/sl_SI/LC_MESSAGES/messages.mo, languages/sl_SI/LC_MESSAGES, languages/sl_SI

# concrete5 Cache Settings
Block Cache - On
Overrides Cache - On
Full Page Caching - Off
Full Page Cache Lifetime - Every 6 hours (default setting).

# Server Software
LiteSpeed

# Server API
litespeed

# PHP Version
5.4.36

# PHP Extensions
bcmath, calendar, Core, ctype, curl, date, dom, ereg, exif, filter, ftp, gd, gettext, hash, iconv, imagick, imap, intl, ionCube Loader, json, libxml, litespeed, mbstring, mcrypt, mysql, mysqli, mysqlnd, openssl, pcre, PDO, pdo_mysql, pdo_sqlite, Phar, posix, Reflection, session, SimpleXML, soap, sockets, SPL, sqlite3, standard, suhosin, tokenizer, xml, xmlreader, xmlrpc, xmlwriter, Zend Guard Loader, zip, zlib.

# PHP Settings
max_execution_time - 300
log_errors_max_len - 1024
max_file_uploads - 20
max_input_nesting_level - 64
max_input_time - 300
max_input_vars - 1000
memory_limit - 1024M
post_max_size - 100M
sql.safe_mode - Off
upload_max_filesize - 100M
mysql.max_links - Unlimited
mysql.max_persistent - Unlimited
mysqli.max_links - Unlimited
mysqli.max_persistent - Unlimited
pcre.backtrack_limit - 1000000
pcre.recursion_limit - 100000
session.cache_limiter - <i>no value</i>
session.gc_maxlifetime - 7200
soap.wsdl_cache_limit - 5
suhosin.cookie.max_array_depth - 50
suhosin.cookie.max_array_index_length - 64
suhosin.cookie.max_name_length - 64
suhosin.cookie.max_totalname_length - 256
suhosin.cookie.max_value_length - 10000
suhosin.cookie.max_vars - 100
suhosin.executor.include.max_traversal - 0
suhosin.executor.max_depth - 0
suhosin.get.max_array_depth - 50
suhosin.get.max_array_index_length - 64
suhosin.get.max_name_length - 64
suhosin.get.max_totalname_length - 256
suhosin.get.max_value_length - 512
suhosin.get.max_vars - 100
suhosin.log.phpscript.is_safe - Off
suhosin.memory_limit - 0
suhosin.post.max_array_depth - 50
suhosin.post.max_array_index_length - 64
suhosin.post.max_name_length - 64
suhosin.post.max_totalname_length - 256
suhosin.post.max_value_length - 1000000
suhosin.post.max_vars - 1000
suhosin.request.max_array_depth - 50
suhosin.request.max_array_index_length - 64
suhosin.request.max_totalname_length - 256
suhosin.request.max_value_length – 1000000a
suhosin.request.max_varname_length - 64
suhosin.request.max_vars - 1000
suhosin.session.max_id_length - 128
suhosin.upload.max_uploads - 25

Thanx...

I note that;

# Server Software
LiteSpeed

# Server API
litespeed

# PHP Version
5.4.36