I want to display entries in a specific custom order in Craft. For example entry Id 1, then Id 5, then Id 3. How can I do that?
Try using a structure. You can reorder them in the CP.
{% for entry in craft.entries.section('your_structure') %}
{{ entry.title }}
{% endfor %}
Another option if you can't use structures is to have a global that is a collection of entries, and use that global to determine which entries and in what order.
{% for e in myGlobal.myEntries %}
{{ e.title }}
{% endfor %}
Structures aren't available in the free version of Craft, but a useful workaround is to simply manipulate the entry published date to accomplish a custom sort, as Craft orders entries from newest to oldest by default. It's a hack, but it's useful in a pinch.