Hello!
I am Wolf for short and I am a jungle main. Warwick was my favorite jungler in season 4 and with the new items in season 5 he is only better. My problem when starting out was I could never find a good, full build for him so that's why I am making this.
This is my first guide so please bear with me, but my goal is to share what I think is the best Warwick build in the new season 5.
It is already established that Warwick is undeniably the BEST jungle in season 5 and this build will hopefully help you to maximize his potential.

Thanks for reading.

Pros
+ Best Sustain in jungle
+ Best Duelist (this build maximizes that)
+ Early dragon kills and early Nashor control
+ Superior mid and late game
+ Hunter's Call gives a team buff which is great for team fights

Cons
- no gank potential pre-level 6
- falling behind will cripple you (true of most jungles and laners)
- no range except for his ult (problematic if an enemy team has several ranged champions)

STARTING ITEMS

Hunter's Machete- this is a must obviously (seriously you're a jungle). It allows you to dominate jungle monsters and will build to your main jungle item.

Scrying Orb- this is my personal choice just because it can be used from a distance to spy on the enemy jungle for counter-jungling. Sweeping lens and warding totem are also good it's just your preference.

Note- this is literally all you need. Warwick's sustain will keep you alive so no need for health potions. Early jungle game your W (Hunter's Call) is what keeps you alive and it is low mana cost so no need for mana potions. Save your gold for later for the Devourer.

CORE ITEMS

SKIRMISHER'S SABRE - DEVOURER- this is Warwick's bread and butter. Your goal is to have this built ASAP. 8 minutes is the goal for this item from there you can snowball. It provides that much needed attack speed, couple smite with your ult for an almost certain kill, and the bonus magic damage is Amazing. The reason to build this early is for the devourer buff; every large monster slain gives +1 extra magic damage per basic attack. By getting this early you can start building up that extra magic dmg while still in the jungle (this is equivalent to Nasus q) if you wait until later you wont be in the jungle as much and you wont build as much dmg.

STINGER- this is essential early game because of the attack speed and cooldown reduction. Warwick has decent cooldown lengths but when you really need to gank or 'q' for extra health then this lower cooldown is essential. This also resets your 'w' faster allowing for early dragon takedowns.

BOOTS OF SWIFTNESS- +60 movement speed is great for hunting down low health targets and lane ganking. These also reduce movement slowing effects which is ideal if you need to run away because Warwick is terrible at fleeing (its often better to stay and fight than run). Homeguard is an excellent final build to get to the jungle or a lane after visiting the shop.

TIAMAT- this is your only attack dmg item. Warwick has low early game attack dmg (by end game it's still only about 250) but attack speed makes up for that. Tiamat does give you a good AD boost though and its 'cleave' passive makes jungle clearing a breeze. You should upgrade to the Hydra fairly soon after getting Tiamat.

WIT'S END- this is a classic Warwick item that still holds up in season 5. With your other items Warwick's attack speed is now unbelievably high (allowing for excellent lane defence and clearing). Wit's End also stacks on magic damage which couples with your skirmisher's sabre perfectly. This is a must item for late game kills.

END GAME ITEMS
as far as end game items go you just build Tiamat into the Hydra for extra AD, or depending on how the game is build Stinger into Zephyr for extra AD, attack speed, and movement speed, or build Randuins for extra health, armor, and dmg (if you are behind or are being targeted by enemy ADs).

SITUATIONAL ITEMS
This is just a fan-made guide. I don't have all the answers so if you feel like swapping 1 item for another feel free to test out different things and see what works for you.

As jungle your spell options are fairly obvious: SMITE and IGNITE.

SMITE- this is a must it is the only way you will survive the early jungle. New large monsters have certain buffs from smiting them which are very useful. Also the skirmisher's sabre is useless without smite.

IGNITE- this is my personal go-to spell. It helps to secure a gank if your oponent runs with away towards a nearby turret with little health left just ignite and finish them. This is also perfect if you are dueling an enemy jungle who thrives on sustain because ignite negates self-healing. *also be warned that getting ignited as Warwick is practically a death sentence.

FLASH- this is another common choice, especially for Warwick who is bad at running away, as it allows for an easy escape or to close the distance for a gank. Personally, I say don't bother because your sustain is better than running away and you should use your ult to engage.

Don't bother with any other spell than these 3 because they will be less than useless.

Your goal is very simple: GET TO LEVEL 6.
Until you reach level 6 your gank potential is 0 and you really should not leave the jungle until you are level 6; after that it's gank galore. So..

START:
Gromp (smite) -> Blue Buff -> Wolves -> Krugs (smite) -> Red Buff -> Raptors -> Gromp

EXPLANATION:
taking Krugs first and smiting the big one for 'Heavy Hands' buff is crucial. this will allow you to take on the Raptors after you get the Red Buff. When fighting the wolves the first time attack the two smaller wolves first then the big one otherwise you will end up dead. The same goes for the Raptors the first time: take out 2-3 of the small ones then target the big one. After you fight Gromp you should be level 6 if not jump in a lane and grab the last few xp to get your ult. YOU SHOULD NOT HAVE BACKED YET! When you reach level 6 gank any lane (preferably the one that needs the most help or the enemy with the least health). I usually hit mid or bottom lane. Now you should have enough gold for Devourer if not get the Sabre and 2 Daggers and Boots.

After backing your ult should be back up so go gank another lane. Then return to the jungle, counter-gank, or invade depending on circumstances. As soon as you get the gold back and get the devourer if you didn't your first time back.

You can now safely fight any jungle camp and your goal is to build the Devourer while watching lanes for ganks. At level 9 make sure you have the Devourer, Stinger, and Boots; you can now solo the dragon. With the new jungle, Dragon control is vital and it is your job as jungle to make sure your team gets the buffs.

SMITE- after level 7/8 you shouldn't need smite in the jungle and you should save it for using it on your enemies before engaging them (usually ult). the exception being the Dragon and the Nashor.

Your first 6 levels should go in this pattern 'W'->'Q'->'W'->'Q'->'E'->'R'

Delaying your E until level 5 is obvious because you aren't ganking until lvl 6 and it has no other purpose than to help gank. After these 6 levels you have more freedom but I strongly encourage you to follow the list above as it will help you with early dragon domination.

Some guides may put 1 point in Warwick's 'E' at level 4-5 and then not again until level 12 but taking the second point at 10 is better for chasing down kills. Granted if you take Flash instead of Ignite then waiting until level 12 is fine.

If you read all of this then Thank You. Any feedback would be great, this is my first Guide so I am always looking to improve it. Warwick is a great champion choice and I hope this will help you utilize him.

-Wolf

p.s. sorry it's not as pretty as some of the other guides out there. my inexperience is showing.