If I had a spare $10,000, here are five ASX shares I'd invest in. And they're all tipped to climb higher over the next 12 months.

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AMP Ltd (ASX: AMP)
While 2026 so far has been a series of bad news events for the AMP share price, it looks like the stock could shift course and begin soaring again over the next 12 months.
This week, AMP confirmed it will undertake an on-market buyback of up to $150 million of ordinary shares and Blair Vernon has officially stepped into the CEO role. Sentiment could well follow suit.
Analysts have a strong buy rating on AMP shares and tip a potential 33% upside to $1.75 per share, at the time of writing.
Capstone Copper Corp (ASX: CSC)
Capstone shares have crashed 40% over the past six weeks driven by rising operating costs and production disruptions. But I think rising copper prices could renew some investor confidence in the ASX copper company's shares.
Capstone has confirmed 2026 production guidance of 200,000 to 230,000 tonnes of copper at C1 cash costs of US$2.45 to US$2.75 per pound. It also expects largely stable production in 2026, with growth anticipated from Mantoverde Optimised from 2027.
Analysts tip the shares to jump 45% higher to $15.10 a piece, at the time of writing.
EVT Ltd (ASX: EVT)
EVT is an Australian provider of entertainment, hospitality, tourism, and leisure-related services in Australia, New Zealand, and Germany. The company announced it has completed $750 million in refinancing this week.
The refinancing, together with EVT's non-core asset divestment program, is expected to give the business more financial flexibility and aid a business shift towards the hotel and accommodation sector.
Analysts tip a potential 20% upside to $15.90 a piece, at the time of writing.
Genesis Minerals Ltd (ASX: GMD)
The ASX gold stock's shares have tumbled nearly 27% over the past month after concerns about rising inflation and more interest rate hikes overshadowed gold's traditional safe-haven status.
The metal's price has tumbled from an all-time high on the 1st of March. But Genesis Minerals' has managed to maintain a strong revenue and earnings performance driven by increased production. I think as soon as gold comes back into favor, this ASX share will fly higher.
Analysts tip a potential 60% share price upside to $9.41, at the time of writing.
Newmont Corp (ASX: NEM)
Newmont is another ASX gold share which was oversold in March.
Declining gold prices have weighed heavily on the world's largest gold miner, with its share price down 19% over the course of the month. I think the stock could rebound sharply as the gold price recovers.
Analysts tip a potential 26% upside to $192.20 a piece, over the next 12 months.