Telstra Group Ltd (ASX: TLS) has been a familiar name in Australian investment portfolios for decades.
Many investors own the telecommunications giant for its dividends, but I think there's a bigger question worth considering.
Could Telstra deliver enough earnings growth over the next five years to push its share price considerably higher?
With the company making progress on its long-term strategy, I think it's worth taking a closer look.

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A stronger business than it used to be
One reason I'm optimistic about Telstra's future is the strength of its mobile business.
The company has spent heavily on its network over the years, giving it a competitive position that would be extremely difficult for a new entrant to replicate.
And I think that investment is increasingly paying off. In FY26, Telstra's mobile revenue increased 3.2% to $11.37 billion, supported by higher revenue per customer and continued demand for mobile services.
I like the pricing power that comes with operating a leading network. Customers increasingly depend on reliable mobile connectivity for work, entertainment, banking, and everyday activities. I think many will continue to place a premium on network quality.
And because Telstra already has such a large customer base, relatively modest increases in average revenue can make a meaningful contribution to earnings.
The next phase of growth
I'm also interested in what Telstra is doing beyond its traditional telecommunications services.
Under its Connected Future 30 strategy, management wants to make better use of the company's existing network while expanding its digital infrastructure business.
One example is its Aura Network, which is an intercity fibre project designed to support Australia's growing data requirements.
Telstra has already secured long-term agreements involving major technology companies, including Microsoft, Google, and Amazon Web Services.
As artificial intelligence (AI), cloud computing, and data centres become increasingly important, I think demand for high-capacity connectivity could continue growing.
This gives Telstra another way to generate value from its substantial infrastructure investments. And management is also working to improve efficiency throughout the business.
In FY26, underlying operating expenses fell by $454 million, helping underlying EBITDA after leases increase 4% to $8.3 billion.
I think there's room for these improvements to continue supporting profitability.
What could Telstra shares be worth in 2031?
Telstra's ambitions provide an encouraging starting point. Management is targeting mid-single-digit annual growth in cash earnings through FY30, alongside a sustainable and growing dividend.
If cash earnings were to increase by 5% annually for five years, they would be approximately 28% higher by the end of that period.
That doesn't automatically translate into a 28% share price increase, but it illustrates the potential impact of steady earnings growth.
Telstra has also announced another share buyback of up to $1 billion, which could support earnings per share (EPS) by reducing the number of shares outstanding.
And with its FY26 dividend totalling 21 cents per share, investors are also receiving income while waiting for that growth to emerge.
There are challenges, including competition, substantial network investment requirements, and the need to improve service reliability following recent outages. But I think a combination of rising earnings, disciplined capital management, and growing dividends could deliver attractive shareholder returns.
Foolish takeaway
I would be happy buying Telstra shares with a five-year investment horizon.
I don't expect explosive growth, and the company's valuation will influence how much of its earnings improvement translates into a higher share price.
But I think Telstra has a realistic opportunity to become a more profitable business by 2031. And if management delivers on its strategy, I wouldn't be surprised to see the shares trading significantly higher than today's levels.