try doing:
<?xml version="1.0" encoding="utf-8"?>
<android.support.v7.widget.CardView xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
xmlns:card_view="http://schemas.android.com/apk/res-auto"
card_view:cardElevation="2dp"
card_view:cardCornerRadius="5dp">
<FrameLayout
android:background="#FF0000"
android:layout_width="4dp"
android:layout_height="match_parent"/>
<LinearLayout
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:padding="16dp"
android:orientation="vertical">
<TextView
style="@style/Base.TextAppearance.AppCompat.Headline"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:text="Title" />
<TextView
style="@style/Base.TextAppearance.AppCompat.Body1"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:text="Content here" />
</LinearLayout>
</android.support.v7.widget.CardView>
this removes the padding from the cardview and adds a FrameLayout with a color. You then need to fix the padding in the LinearLayout then for the other fields
Update
If you want to preserve the card corner radius create card_edge.xml in drawable folder:
<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android" >
<solid android:color="#F00" />
<size android:width="10dp"/>
<padding android:bottom="0dp" android:left="0dp" android:right="0dp" android:top="0dp"/>
<corners android:topLeftRadius="5dp" android:bottomLeftRadius="5dp"
android:topRightRadius="0.1dp" android:bottomRightRadius="0.1dp"/>
</shape>
and in the frame layout use android:background="@drawable/card_edge"