こっそりと。

※ add-apt-repository ができないので、以下のコマンドでインストールします。
# apt-get install -y software-properties-common

# add-apt-repository ppa:ondrej/php
以下の通りエラーに。

Co-installable PHP versions: PHP 5.6, PHP 7.x and most requested extensions are included. Only Supported Versions of PHP (http://php.net/supported-versions.php) for Supported Ubuntu Releases (https://wiki.ubuntu.com/Releases) are provided. Don't ask for end-of-life PHP versions or Ubuntu release, they won't be provided.

Debian oldstable and stable packages are provided as well: https://deb.sury.org/#debian-dpa

You can get more information about the packages at https://deb.sury.org

BUGS&FEATURES: This PPA now has a issue tracker:
https://deb.sury.org/#bug-reporting

CAVEATS:
1. If you are using php-gearman, you need to add ppa:ondrej/pkg-gearman
2. If you are using apache2, you are advised to add ppa:ondrej/apache2
3. If you are using nginx, you are advise to add ppa:ondrej/nginx-mainline
   or ppa:ondrej/nginx

PLEASE READ: If you like my work and want to give me a little motivation, please consider donating regularly: https://donate.sury.org/

WARNING: add-apt-repository is broken with non-UTF-8 locales, see
https://github.com/oerdnj/deb.sury.org/issues/56 for workaround:

# LC_ALL=C.UTF-8 add-apt-repository ppa:ondrej/php
More info: https://launchpad.net/~ondrej/+archive/ubuntu/php
Press [ENTER] to continue or ctrl-c to cancel adding it

gpg: keyring `/tmp/tmpli8ajd6a/secring.gpg' created
gpg: keyring `/tmp/tmpli8ajd6a/pubring.gpg' created
gpg: requesting key E5267A6C from hkp server keyserver.ubuntu.com
gpg: /tmp/tmpli8ajd6a/trustdb.gpg: trustdb created
gpg: key E5267A6C: public key "Launchpad PPA for Ond\xc5\x99ej Sur mported
gpg: Total number processed: 1
gpg: imported: 1 (RSA: 1)
Exception in thread Thread-1:
Traceback (most recent call last):
File "/usr/lib/python3.4/threading.py", line 920, in _bootstrap_inner
self.run()
File "/usr/lib/python3.4/threading.py", line 868, in run
self._target(*self._args, **self._kwargs)
File "/usr/lib/python3/dist-packages/softwareproperties/SoftwareProperties.py", line 687, in addkey_func
func(**kwargs)
File "/usr/lib/python3/dist-packages/softwareproperties/ppa.py", line 370, in add_key
return apsk.add_ppa_signing_key()
File "/usr/lib/python3/dist-packages/softwareproperties/ppa.py", line 261, in add_ppa_signing_key
tmp_export_keyring, signing_key_fingerprint, tmp_keyring_dir):
File "/usr/lib/python3/dist-packages/softwareproperties/ppa.py", line 210, in _verify_fingerprint
got_fingerprints = self._get_fingerprints(keyring, keyring_dir)
File "/usr/lib/python3/dist-packages/softwareproperties/ppa.py", line 202, in _get_fingerprints
output = subprocess.check_output(cmd, universal_newlines=True)
File "/usr/lib/python3.4/subprocess.py", line 609, in check_output
output, unused_err = process.communicate(inputdata, timeout=timeout)
File "/usr/lib/python3.4/subprocess.py", line 947, in communicate
stdout = _eintr_retry_call(self.stdout.read)
File "/usr/lib/python3.4/subprocess.py", line 491, in _eintr_retry_call
return func(*args)
File "/usr/lib/python3.4/encodings/ascii.py", line 26, in decode
return codecs.ascii_decode(input, self.errors)[0]
UnicodeDecodeError: 'ascii' codec can't decode byte 0xc5 in position 92: ordinal not in range(128)

以下のコマンドを実行。
# LC_ALL=C.UTF-8 add-apt-repository ppa:ondrej/php
# apt-get update

PHP7 をインストールします。※
# apt-get install php7.0

mysql モジュールも。
# apt-get install php7.0-mysql

インストールは完了したので、モジュールを有効にします。
・先に php5 を無効に。
# a2dismod php5

・php7 を有効に。
# a2enmod php7.0

サービス再起動
# service apache2 restart

なおコマンドラインでは php7 が実行されていました。

# php -v
PHP 7.0.27-1+ubuntu14.04.1+deb.sury.org+1 (cli) (built: Jan 11 2018 23:19:41) ( NTS )
Copyright (c) 1997-2017 The PHP Group
Zend Engine v3.0.0, Copyright (c) 1998-2017 Zend Technologies
with Zend OPcache v7.0.27-1+ubuntu14.04.1+deb.sury.org+1, Copyright (c) 1999-2017, by Zend Technologies

これで php 7 になりました。