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This question already has an answer here:

If a multi class Paladin/ Eldritch Knight cast Shield of Faith, and then as a reaction cast shield, would they get a +7 Bonus to their AC?

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marked as duplicate by NautArch dnd-5e Mar 30 '18 at 12:57

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Yes.

SRD under Spellcasting and Combining Magical Effects (this is also in the PHB p205) emphasis mine.

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.

Both these spells give flat bonuses so it is easy enough to see the effects stack.

Other spells like Mage Armor and Barkskin have different wordings and although they would stack with the two spells you are referencing have different interactions with other features and spells as detailed in this question and this one.

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Yes

But only for one round. See PH page 205 "Combining Magical Effects":

The effects of different spells add together while the durations of those spells overlap.

Shield gives you +5 bonus to AC and Shield Of Faith gives you another +2 bonus to AC. These two bonuses do stack. Compare this with the Mage Armor spell effect, which modifies your base AC:

The target's base AC becomes 13 + its Dexterity modifier.

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