Using SQL to reorder items in a list view - is this efficient?
Enum
First of all, instead of an int orderByType, I would use an enum.
enum SortOrder {
    NEWER(&quot;date(&quot; + SomeConstant.KEY_DATE + &quot;) desc&quot;),
    OLDER(&quot;date(&quot; + SomeConstant.KEY_DATE + &quot;) asc&quot;),
    ...;
    private SortOrder(String order) {
        this.order = order;
    }

    public String getOrder() {
        return this.order;
    }
}

This will clean up your getAllTransactions method:
public Cursor getAllTransactions(SortOrder orderByType) {
    return getAllTransactions(orderByType == null ? null : orderByType.getOrder());
}


Database vs. Application
I feel that is OK to let the database deal with this. There is a positive aspect of letting it be handled in the application: If the application deals with it, then you can reorder the elements without querying the database.
However,

The list is small (5 records at the most)

I think either way will work just fine. If it is common to reorder the list, then I would let the application deal with it. Although your enum SortOrder needs quite a lot of more code to work directly with a List&lt;T&gt;.
If you want to use an enum and reorder inside the application, then I would let the enum take a Comparator&lt;T&gt; in the constructor and create an anonymous inner class for each enum value.