A very nice mountless variant! This coming from the guy who has a slightly less front-loaded and more mount specific paladin variant of his own with bonus divine/mounted feats every 5 levels.
Only recommendations I could make are for the 5th level spell list. Perusing the Paladin Spell list we see that as a couple general rules of thumb for spells on the Paldin spell list appear:
Healing-type spells are taken from one level lower (
cure serious wounds is a 4th level paldin spell but a 3rd level cleric spell) and martial/defeating evil-type spells are taken from one level higher (dispel evil is a 4th level Paladin spell but a 5th level cleric spell), and defensive/protective spells are generally of the same level (death ward is both a 4th level Paladin and Cleric spell).
Here's the 5th level spell list you've got:
Banishment,
Flame Strike,
Hallow,
Heal,
Planar Ally,
Raise Dead,
Spell Resistance,
True Seeing.
Banishment is great for fighting those evil outsiders (a 6th level cleric spell) and is well suited!
Flame Strike being a martial/defeat evil-type spell looks to be a great choice!
Hallow is a nice spell to add to the list, very appropriate, it sort of fits in the defensive/protection type of spells and being 5th level cleric spells fits well as a paladin 5th level spell.
Planar Ally (a 6th level Cleric spell) can be potentially be described as a martial-type spell and is a reasonable choice, especially when the ally may ask instead for a quest rather than payment for their aid.
Spell Resistance meets the requirment being a 5th level cleric spell and a defensive/protective type, good there too.
True Seeing also fits pretty well here, seeing through the lies and deception of illusions.
Heal I'd have to recommend not including on this list being a 6th level cleric healing-type spell. A Paladin's 5th level spell should only inlcude 4th level cleric healing spells; in this case it should be Cure Critical Wounds, not Heal, unfortunately.
Raise Dead is also probably inappropriate for the same reason, though less so (being a 5th level Cleric healing-type spell, lower than Heal's 6th level). Perhaps you could leave raise dead on the spell lsit and add the stipulation that a paladin may only raise those that worship their patron deity? This would lower the spells power abit and be more than appropriate for a Paladin, given the power to raise others but not just anyone, only those that serve and worship the paladin's deity in some way, that'd actually be pretty cool. For what it's worth I'd suggest a minor alteration to the 5th level spell list (changes in brown):
Paladin 5th level Spells:
Banishment,
Cure Critical Wounds,
Flame Strike,
Hallow,
Planar Ally,
Raise Dead (
those of faith only),
Spell Resistance,
True Seeing.
Very minor changes. I'm now going to have to offer this mountless variant paladin to my players heh. Snag and thanks!