The whole point of investing is to deploy your hard-earned cash into wealth-producing assets in order to make your money make more money. ASX shares are one of the best asset classes to employ in this endeavour.

For more than a century, the ASX has compounded Australian investors' wealth. Although the future is always uncertain, it's hard to imagine that this won't continue well into the future.

So we know that ASX shares can help us build wealth. But how exactly does this work? And how can we invest $5,000 and turn it into $50,000 or more?

Compounding with ASX shares

I won't sugarcoat this: Effectively building wealth using ASX shares takes a lot of time. Otherwise, there'd be a lot more millionaires in Australia than there are today. It also requires a great deal of discipline and long-term thinking. Turning a $5,000 investment into $50,000 won't happen overnight.

But it can be done.

The first step is to understand the power of compounding and how you can harness it to grow your capital exponentially.

ASX shares are fantastic investments precisely because of their potential to compound. In other words, earn interest on interest. Under the rule of 72, your money can expect to double roughly every 10 years if you achieve a 7% rate of return.

In this way, $1 can become $2, then $4, $8 and so on. Successful compounding means that your money grows by more each year than it did in the previous one.

The best investors tend to individually pick out stocks that have a higher capacity to deliver returns than average.

But you don't need to be the next Warren Buffett in order to slowly but steadily build wealth.

Building wealth over time

The next step is to find the right investments. Let's assume we invest $5,000 into a simple ASX shares index fund. This will give us an average return from the market of sorts, given it holds the largest 200 or 300 shares on our stock market. That's everything from Commonwealth Bank of Australia (ASX: CBA) and Telstra Group Ltd (ASX: TLS) to JB Hi-Fi Ltd (ASX: JBH) and AGL Energy Ltd (ASX: AGL).

One example of an index fund in this vein is the iShares Core S&P/ASX 200 ETF (ASX: IOZ). Since its ASX inception in 2010, this index fund has returned an average of 8.28% per annum (that's growth plus reinvested dividend payments).

If you invested $5,000 in this fund and got that same rate of return (which is not guaranteed, of course), it would take around 28 years to turn $5,000 into $50,000.

That's all well and good, but it also assumes we'll have no capacity to continue investing in ASX shares. If an investor could stump up an extra $50 every week, they could cut that 28 years down to just ten. If they could stump up $100 a week, we'd be looking at six and a half years.

Successful investing doesn't have to be rocket science. All you need to do is find the right ASX shares (or index funds) and be disciplined and patient.