* Cink flies high with 64 at Torrey Pines
* Seven-times winner Woods starts out in level par
* Mickelson battles back problems for a 69 (Updates at end of round)
Jan 23 (Reuters) - Stewart Cink, seeking his first PGA Tour title in five years, charged into a one-shot lead at the Farmers Insurance Open on Thursday as Phil Mickelson also moved into early contention despite nursing a troublesome back.
Mickelson, who frequently winced at the top of his backswing because of muscle pain down his side, carded a three-under 69 on the easier North Course while seven-times champion Tiger Woods opened with an even 72 on the brutal South layout.
Cink, who has not triumphed anywhere since his playoff victory over Tom Watson in the 2009 British Open at Turnberry, fired a flawless 64 on the North to seize control of the PGA Tour event at picturesque Torrey Pines outside San Diego.
The 40-year-old Cink birdied four of his last six holes to end a mainly sunny day which began with a fog delay of 30 minutes one stroke in front of fellow American Gary Woodland, who also started out on the North.
Australians Jason Day and Marc Leishman, South African Tyrone van Aswegen and American Jim Herman opened with 66s while American Pat Perez, with a 67, was the only player in the top 16 who played on the more difficult South layout.
Tour veteran Cink was delighted with his opening round, despite totalling just one birdie on the four par-five holes.
"If you drive it well on the North Course, you're going to have birdie opportunities and I drove it very well most of the day," the tall American told Golf Channel.
"It was just a different game from the short grass out there. You've got some shorter holes and I took advantage of a lot of those holes ... the par-fives, I didn't play those very well. It was a very calm, very relaxed kind of round."
Cink, a six-times winner on the PGA Tour, knows he will face a very different challenge in Friday's second round on the South Course, which played almost four strokes harder than the North on Thursday.
"It's definitely a tale of two golf courses here," he smiled. "The South we all know is one of the most difficult courses on the tour and it pretty much requires all facets of the game to be on.
"I have been playing fairly well this year so I am looking forward to the challenge. It's a big golf course to really test yourself and see where you stand this time of year."
Woods, competing in his first tournament of the year, offset two birdies with two bogeys on a South layout playing tougher than usual because of firm conditions, narrow fairways and thick rough.
"Well, even par's not too bad, but I didn't play the par-fives worth a darn today," said the world number one, who clinched last year's Farmers Insurance Open by four shots in a fog-delayed Monday finish.
"I played them even par, parred all of them ... to try to get any kind of scoring on the South course you've got to take care of the par-fives because there's not a lot of holes you can make birdies here.
"It (the South) has got to be playing right around three shots easier, so I'm going to have to go out there and get it a little bit tomorrow to not be so far behind come Saturday or Sunday."
San Diego native Mickelson, a three-times champion at Torrey Pines, mixed four birdies with a lone bogey to climb the leaderboard and was thankful he had played his opening round on the less daunting North.
"I kind of milked my way around the golf course and I was able to do that on the North Course because the penalty wasn't as severe as it is on the South," the American left-hander said.
"I am able to kind of get it up by the green and get up and down and salvage par. I made a couple of birdies but it won't hold up on the South Course so I've got to get it better."
Asked to explain what was wrong, Mickelson replied: "From the top (on the swing), it just kept locking up and giving me a shooting pain. I kind of flinch.
"If I overdo it, it's just prone to getting a little bit tight. It's just a muscular thing. My back feels fine, it's just a muscle on the side. I think it will go away in a short period of time. I don't think it's anything serious."
However, Mickelson said he would consider withdrawing from the event if his muscle pain did not respond sufficiently to treatment over the next 24 hours. (Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)