Use the bear's Con modifier + your proficiency bonus: +6 total
The druid's Wild Shape feature specifies how your new form's statistics interact with those of your regular form:
While you are transformed, the following rules apply:
Your game statistics are replaced by the statistics of the beast, but
you retain your alignment, personality, and Intelligence, Wisdom, and
Charisma scores. You also retain all of your skill and saving throw
proficiencies, in addition to gaining those of the creature. If the
creature has the same proficiency as you and the bonus in its stat
block is higher than yours, use the creature’s bonus instead of
You retain the benefit of any features from your class, race, or
other source and can use them if the new form is physically capable
of doing so. [...]
In this case, you're using Wild Shape to turn into a brown bear. The brown bear has a Constitution score of 16 (a +3 modifier), and is not proficient in any saving throws. Your regular human form also has a Constitution score of 16 (a +3 modifier) - but your Resilient feat gives you proficiency in Constitution saving throws. Since you're level 5, your proficiency bonus is also +3, for a total modifier of +6.
Even if you didn't retain the benefit of features from your race/class (in this case, your feats), the Wild Shape feature explicitly says you retain your own saving throw proficiencies.
Now, the question of what your total Constitution saving throw modifier then becomes might seem a little confusing at first, because you may wonder whether your proficiency bonus is retained or not. However, this is clarified in an episode of Dragon Talk and a few unofficial tweets by rules designer Jeremy Crawford (cited in this answer by Bash to a related question about what values are recalculated in Wild Shape).
First, Crawford clarified the intent of the first bullet point of Wild Shape in this series of tweets in 2015:
Debate resolution. Druid in wildshape. Keep prof bonus to attack or use beast's stats unmodified?
A druid in beast form uses his or her proficiencies, except when the beast has the same proficiency with a higher bonus.
That doesn't answer the Q. Druid is not prof in claw/bite. Black bear form, +3 for bear, or prof+2 for druid w/ bear str?
The intent is that the druid uses the bonus in the beast's stat block for any proficiency the druid lacks.
Second, Crawford stated the following in the Sage Advice segment of the April 6, 2017 episode of Dragon Talk, in response to a question about what happens if you Wild Shape into a creature with a lower modifier to a skill like Stealth:
You get to use your proficiency bonus. But you do use the creature's Dexterity modifier. This is where it gets tricky. Use your proficiency bonus for anything where you're both proficient, but only if yours is higher - but you use the physical stats of the beast.
The same logic applies to saving throws.
Finally, Crawford reiterated the meaning of the first bullet point of Wild Shape in this 2018 tweet:
I have seen two different tweets of yours, so I am looking for clarity. My lvl 5 druid has a +3 prof bonus, when I shape into a brown bear I have a str of 19 and an attack bonus of 5. Do I add my druid prof bonus to attack bringing it to +7? Thank you!
The Wild Shape feature does not let you add your proficiency bonus to the proficiency bonus of your beast form. The first bullet of the class feature details which proficiency bonus you use (PH, 67).
- If the beast's proficient in a physical saving throw (Str/Dex/Con)
and its modifier to the saving throw is higher than yours, just use
the beast's saving throw modifier (whether or not you're proficient).
- If the beast's not proficient and neither are you, use the beast's
saving throw modifier. Simple.
- If the beast's not proficient but you are, then you add your
proficiency bonus to the beast's corresponding ability modifier.
In this case, the last scenario is applicable. You're proficient in saving throws, but the brown bear is not. Thus, you add your proficiency bonus of +3 to the brown bear's Constitution modifier of +3, for a total of +6.
(And as detailed in this linked question, you do retain the benefit of your War Caster feat, so you have advantage on your Constitution saving throws to maintain concentration - even in Wild Shape.)