So if I go Duskblade level 5, then get Abjurant Champion level 5, then go back to Duskblade, will I get level 11, or level 6 for Duskblade?
The Abjurant Champion adds 5 levels to Duskblade, so I would assume that for the next level I would level into Duskblade as if I am a level 10 Duskblade going into level 11.
Some prestige classes, like Abjurant Champion, advance specific features of the base class (in this case, spellcasting).
From Abjurant Champion, emphasis added:
At each level, you gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in an arcane spellcasting class to which you belonged before adding the prestige class level. You do not, however, gain any other benefit a character of that class would have gained. If you had more than one arcane spellcasting class before becoming an abjurant champion, you must decide to which class to add each level for the purpose of determining spells per day, caster level, and spells known.
So when you take your next level of Duskblade, you will be Duskblade level 6, and get the class features listed at 6th level (Spell Power +2), but you will have the spellcasting of an 11th-level Duskblade (gaining two 3rd-level spells per day).
You are misunderstanding how levels work in general. When you gain a level, you put it into a class and become level X+1 in that class. Each class functions completely independently of each other except for specific abilities that say they stack with other classes.
In your example, when you add a new level to Duskblade, you become an Duskblade 6/Abjurant Champion 5. Now, Abjurant Champion does not "add to" Duskblade levels. It only has this statement under its Spellcasting ability.
At each level, you gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in an arcane spellcasting class to which you belonged before adding the prestige class level. You do not, however, gain any other benefit a character of that class would have gained. If you had more than one arcane spellcasting class before becoming an abjurant champion, you must decide to which class to add each level for the purpose of determining spells per day, caster level, and spells known.
So the Abjurant Champion levels add to your Duskblade caster levels allowing you to cast as an 11th level caster (and the other benefits listed) - but that's it, nothing else, certainly not the same as being a Duskblade 11. See Class level vs. Character level vs. "my" level for more of an explanation of class level vs character level vs spellcasting level.
Going from Duskblade 5/Abjurant Champion 5 and taking another level of Duskblade, you would be Duskblade 6/Abjurant Champion 5 (not Duskblade 11/Abjurant Chamion 5). Class levels are always taken consecutively.
But what about the Champion spellcaster levels that count as Duskblade spellcaster levels? After levelling up to Duskblade 6, your level 5 Champion benefits would be applied on top of those 6 levels of Duskblade and recalculated. Your spellcaster level would be 11, but you'd be Duskblade 6.
