Remember Aesop's fable about the tortoise and the hare? Many investors would view dividend stocks as more similar to the tortoise than the hare. They win by slowly plodding along.

However, there are exceptions among them that might not be so tortoise-like in the near future. Here are three dividend stocks that could realistically skyrocket over the next five years.

1. Digital Realty Trust

You might say that Digital Realty Trust (DLR -2.76%) has been like a hare running backward over the last 12 months. Shares of the real estate investment trust (REIT) have fallen by more than 20% during the period. However, I think Digital Realty Trust should rebound in a huge way over the next few years.

Like many other REITs, Digital Realty Trust's share price has been dragged down in part by the impacts of rising interest rates. Economic uncertainty hasn't helped, either. But these are only temporary issues. Organizations will continue to need the data centers that Digital Realty operates. 

New CEO Andy Power even suggested recently that Digital Realty Trust "may now be on the precipice of the next wave of demand that will drive our sector for the next decade." He was referring to the advances in artificial intelligence (AI) that have made headlines in recent months.  

This could bode well for Digital Realty's ability to grow its dividend in the future. The company's dividend yield currently stands at nearly 4.9%. It has increased its payout for 17 consecutive years.

I wouldn't count on Digital Realty delivering tremendous returns for shareholders until interest rates begin to come down. However, that should happen eventually. 

2. Medical Properties Trust

Medical Properties Trust (MPW 18.80%) is another REIT that hasn't been winning any races lately. Its shares have plunged by more than 60% over the last 12 months. And the surge of momentum it enjoyed earlier in 2023 has also evaporated.

Higher interest rates are only part of the healthcare REIT's problems. Some of Medical Properties Trust's hospital operator tenants face financial challenges. CFO Steven Hamner revealed on the company's fourth-quarter conference call that Prospect Medical didn't pay its full rent in January or February. The low end of the REIT's 2023 guidance range even factors in the possibility that Prospect won't pay any rent this year.

But Medical Properties Trust has weathered such storms in the past and emerged in good shape. I think it will do so again. The company remains confident that it will be able to recover all of its investments and deferred rent from Prospect. Also, the overall financial outlook for hospital operators continues to improve. 

In the meantime, some investors could find Medical Properties Trust's dividend yield of almost 14.9% too tempting to ignore. Considering the headwinds it faces, investors shouldn't expect the healthcare REIT to increase its payout anytime soon. However, Medical Properties Trust should be able to keep funding its dividend at current levels, at least over the near term.

3. Occidental Petroleum

Unlike Digital Realty Trust and Medical Properties Trust, Occidental Petroleum (OXY -0.97%) has delivered a solid share price gain over the last 12 months. Warren Buffett probably deserves some of the credit: He continues to buy the oil stock hand over fist for Berkshire Hathaway's portfolio.

I think Buffett's buying could keep driving Occidental's shares higher. Berkshire Hathaway currently owns 23.1% of the oil and natural gas company, but has secured regulatory approval to acquire up to 50%.

Occidental stock remains relatively cheap, with shares trading at only 8 times expected earnings. The company should have solid growth prospects as it expands into carbon capture and sequestration, a market that could be worth trillions of dollars in the future.

Investors might not be overly impressed with Occidental's dividend yield of around 1.2%. However, those dividends add up over time.