diff --git a/.travis.yml b/.travis.yml
index dbce01c..530e6c9 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,8 +1,6 @@
 language: php
 
 php:
-  - 5.5
-  - 5.6
   - 7.0
   - 7.1
   - 7.2
@@ -14,17 +12,17 @@ cache:
 matrix:
   fast_finish: true
   include:
-    - php: 5.6
+    - php: 7.0 # Laravel 5.0 requires Mcrypt, but it is deprecated as of PHP 7.1
       env: ILLUMINATE_VERSION=5.0.* TESTBENCH_VERSION=3.0.* PHPUNIT_VERSION=4.*
-    - php: 7.1
+    - php: 7.2
       env: ILLUMINATE_VERSION=5.1.* TESTBENCH_VERSION=3.1.* PHPUNIT_VERSION=5.*
-    - php: 7.1
+    - php: 7.2
       env: ILLUMINATE_VERSION=5.2.* TESTBENCH_VERSION=3.2.* PHPUNIT_VERSION=5.*
-    - php: 7.1
+    - php: 7.2
       env: ILLUMINATE_VERSION=5.3.* TESTBENCH_VERSION=3.3.* PHPUNIT_VERSION=5.*
-    - php: 7.1
+    - php: 7.2
       env: ILLUMINATE_VERSION=5.4.* TESTBENCH_VERSION=3.4.* PHPUNIT_VERSION=5.*
-    - php: 7.1
+    - php: 7.2
       env: ILLUMINATE_VERSION=5.5.* TESTBENCH_VERSION=3.5.* PHPUNIT_VERSION=6.*
     - php: 7.2
       env: ILLUMINATE_VERSION=5.6.* TESTBENCH_VERSION=3.6.* PHPUNIT_VERSION=7.*
@@ -32,7 +30,6 @@ matrix:
 sudo: false
 
 before_install:
-  - composer self-update
   # Disable XDebug to speed up Composer.
   - cp $HOME/.phpenv/versions/$(phpenv global)/etc/conf.d/xdebug.ini /tmp
   - phpenv config-rm xdebug.ini
diff --git a/composer.json b/composer.json
index 5ce6085..e6b9d15 100644
--- a/composer.json
+++ b/composer.json
@@ -16,7 +16,7 @@
         }
     ],
     "require": {
-        "php": ">=5.5",
+        "php": ">=7.0",
         "laravel/framework": ">=5.0,<5.7",
         "jenssegers/optimus": "^0.2.2",
         "phpseclib/phpseclib": "^2.0"