Here's where I would invest $5,000 right now in ASX shares

If I were investing $5,000 into ASX shares right now, these are the ones I'd pick including Webjet Limited (ASX:WEB).

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Many share markets and asset classes are trading at all time highs, so I think we need to be careful about which ASX shares we're buying.

Indeed, right now the All Ordinaries (ASX: XAO) Index is above 7,000 for the first time ever. Share markets are meant to break records. Many market commentators may be a bit surprised it's taken the ASX this long to get to 7,000.

Inflation and rising populations should mean that many businesses naturally grow their earnings and share prices over the long-term. Here are the shares I'd want to buy right now:

Webjet Limited (ASX: WEB – $1,500 

The Webjet share price is already up 2.5% in 2020 but I think there could be plenty more to come this year. The B2B WebBeds division could help Webjet grow its FY20 underlying earnings before interest, tax, depreciation and amortisation (EBITDA) by 26% to 34% with organic growth of 16% to 23%.

Thomas Cook's collapse will be a drag on the FY20 statutory result, but FY21 and beyond look very promising. There's talk of a potential takeover with how low Webjet's share price currently is.

Webjet is valued at 15x FY21's estimated earnings.

PM Capital Global Opportunities Fund Ltd (ASX: PGF) – $2,000 

This is a listed investment company (LIC) that has been operating for several years and it focuses on global shares, as the name might suggest.

It has been a solid performer. After fees it has returned 30.3% this year, 13.8% per annum over the past three years and 12.3% per annum since inception. Some of its current holdings include Visa, Bank of America, KKR & Co and Freeport-McMoRan Copper.

Almost a third of its portfolio is invested in global banking and it has a relatively new focus on copper with expectations of a recovery.

I only like buying LICs when they are trading at a discount to their net tangible assets (NTA) to make up for the fees. PM Capital Global Opportunities is currently trading at a 14% discount to the NTA at 3 January 2020.

Future Generation Investment Company Ltd (ASX: FGX) – $1,500 

Future Generation is another LIC, except this one is very different to all other LICs (apart from its globally-focused sibling LIC).

This LIC doesn't charge any fees, instead it donates 1% of net assets to youth charities each year. Instead of investing in individual shares itself, it invests its money into ASX-focused fund managers. These fund managers work for free for Future Generation.

Some of these fund managers try to focus on delivering absolute, or specifically positive, returns. This has led to Future Generation growing with less volatility than the overall market.

Since inception in September 2014 to November 2019, its gross investment returns have been 9.8% per annum compared to the All Ordinaries Accumulation Index's return of 8.7% per annum.

It's currently trading at an 8% discount to the NTA at November 2019.

Foolish takeaway

I think each of these shares have attractive features with good growth prospects. Webjet could be the best performer in 2020, but I like the clear discounts offered by PM Capital & Future Generation with their investment flexibility.

Motley Fool contributor Tristan Harrison owns shares of FUTURE GEN FPO and PM Capital Global Opportunities Fund Ltd. The Motley Fool Australia has recommended Webjet Ltd. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Scott Phillips.

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