Even though the company has had significant successes in those five years — nearly a billion iPhones sold and both revenue and profits more than doubling — Cook's legacy is likely to be defined more by what he does in the next five years, analysts say.
Though Cook has yet to prove he can be as innovative as the charismatic Jobs, he has successfully steered the franchise and maintained its position as the world's most valuable company.
"Historically, founder-led companies go through existential crises after the founder is gone," said Asymco analyst Horace Dediu. "The fact that Apple didn't implode, but has grown, means mission accomplished."
Apple's stock is up 105 percent since Cook stepped into the CEO role, but has slid 3 percent over the past year. The S&P 500 is up 88 percent and 11 percent in those respective periods. In Apple's most recent quarterly results, revenue declined 14.6 percent — a second quarterly decline following 13 years of growth. With this shift, Cook's legacy hangs in the balance.
"Investors may have hoped for new product categories to sustain growth because — as you know — the company is not growing at the moment," said BTIG analyst Walter Piecyk.
Though some investors will want more, Cook has far exceeded what he was asked to do by keeping the iPhone franchise intact and growing, said Piper Jaffray analyst Gene Munster. Cook's operational ability, which has enabled Apple to seamlessly roll out new products globally, is second to none, Munster said.
"We haven't seen as much on the innovation side, and that's really what we're going to learn about Tim Cook over the next five years," said Munster. "It's the things under his guidance, including augmented reality and, potentially, automotives." (Munster has an overweight rating on the stock and a $151 price target. It was trading below $109 on Monday.)
Under Cook, Apple has released one entirely new product: Apple Watch. The device has delivered billions of dollars in revenue, opened up an entirely new product category, and laid the groundwork for the company to deliver wellness and health services.
"They took a risk with Apple Watch, which I think is a phenomenal product," said Drexel Hamilton analyst Brian White. (White has a buy rating on the stock, the firm's top pick for the second half of the year, and a $185 price target.)
Cook must walk a fine line between shipping new products without rushing to market, something he has been judged harshly for by some industry insiders.
"I don't think Jobs would have approved such an early launch, though I do think it will grow nicely and be a great product," said Dediu. "But it didn't have the app system ready for launch."
Apple sold 1.6 million watches in the second quarter of 2016 and had 47 percent of the wearables market, according to IDC, but the product has not taken off as well as some investors had hoped. Users, analysts and carriers would like to see Apple decouple the watch from the phone, something that is not expected to happen this product cycle.
So far, the real standout for Munster has been Cook's success in expanding Apple's services business — things like iCloud, iTunes and Apple Pay — which grew 19 percent last quarter. Services will be the size of a Fortune 100 company by next year, Cook has said.
"Where I think it's been underwhelming on the hardware side, which of course is where they make their money. The technology is just not there to really get the Watch away from the iPhone yet," Steve Milunovich, managing director at UBS, told CNBC's " Power Lunch " on Monday.
He added that Jobs was once against the App Store that has done so well for Apple. "Where I think they've done a good job is on the services side, as you call it, or as we put it, the platform side," Milunovich said.
Some attempts to grow Apple's services business have been less successful. For example, the company bought Beats Music for $3 billion in 2014. The deal was a rare high-profile acquisition for the company that delivered executive talent, and was accompanied by talk of new music experiences. Apple Music — a new streaming service — was launched in 2015 but has so far failed to gain much traction, said Piecyk.
Cook has the opportunity to further leverage Apple's devices to grow revenue from services, said White. For example, Apple TV could be used to sell services — like Mandarin lessons or cooking classes — to consumers at home, he said.
Cook is also credited with opening up new markets for Apple's products. He has forged partnerships with enterprise giants IBM , Cisco and SAP in order to better serve enterprise customers, and grown Apple's footprint in emerging markets. The number of stores in the Chinese marketplace increased from four to 41 during his tenure. Cook recently visited India, which represents a giant opportunity for the company, said White.
"Apple's a very different company today, obviously, than four or five years ago," Milunovich said. "[Cook's] had to deal with the FBI situation , moving into China and India, shareholders demanding dividends and buybacks — which Jobs didn't have to deal with at the time."
One thing investors are watching closely is how much Apple is spending on research and development. R&D investment is expected to increase this year to $10.5 billion — 4 percent of revenue — according to Munster. That level of investment should be coupled with greater innovation than Cook has so far delivered, said Piecyk.
"You have to launch new products — it's fine to spend the money — but until you see them there's really no clarity on what he has been doing," Piecyk said. (Piecyk has a buy rating on Apple and a $124 price target.)
Under Cook, Apple has continually updated the iPhone line but has not delivered great leaps in innovation, he said. (iPhone sales were down 23 percent in the company's most recent earnings report.) The iPhone 6, launched in 2014, delivered the larger screen consumers had been clamoring for, but Apple lost out to competitors by waiting too long, analysts agree.
"He's built a great company — but he's not a visionary," Andy Cunningham, whose PR firm worked with Jobs, told CNBC's " Squawk Alley " on Monday.
An example of the sort of innovation that analysts would like to see would be a phone that doubles as a tablet by flipping open to double in size, said Munster. He is bullish about the innovative steps Cook may take over the next five years to drive iPhone growth.
Though Apple is notoriously secretive about what its engineers are working on, Cook has said he sees the development of augmented and virtual reality — powered by smartphones — as a prime opportunity. On the company's most recent earnings call Cook said Apple is investing in artificial intelligence and virtual reality. Apple now has 218 employees working on augmented reality, up 18 percent in the past year, according to Munster.
"Augmented reality and virtual reality could be something that would allow the platform to be even richer and sustain the iPhone going forward," said Dediu.
Cook's biggest opportunity to make his mark on Apple's business could be in developing an autonomous car, said Dediu. Cook has not spoken publicly about this, but it is widely believed that Apple is working on a car, which has the potential to revolutionize the auto industry.
"There are obstacles, such as getting the supply networks put together and ramped up," said Dediu. "But I think there is already a prototype. However, they will not launch until they can quickly build significant volume."
Apple's hardware, software and design chops make it uniquely well-positioned to build a car that consumers would want to buy, said White. Apple has the advantage of being unencumbered by legacy thinking and union workers — unlike traditional automakers — and could hook the car into its existing ecosystem, he said.
"They are going to pick and choose what markets they want to pursue," said White. "In 10 years we are not going to say Apple is solely reliant on the iPhone."
Apple did not respond to a request for comment.