The firm says it will use a two-stage recruitment challenge, to be found on the Gorillaz mixed reality app, as an "innovative recruitment tool".
The first part involves virtually assembling the Jaguar I-PACE Concept, an all-electric five-seater sports car.
The second part involves a series of code breaking puzzles.
"As the automotive industry transforms over the next decade, fuelled by software innovation, we have to attract the best talent and that requires a radical rethink of how we recruit," said Alex Heslop, head of electrical engineering at the car firm.
"Here we've found an engaging way to recruit a diverse talent pool in software systems, cyber systems, app development and graphics performance. It will be the first of its kind."
Gorrilaz female guitarist, Noodle, is already Jaguar's Formula E Racing's ambassador.
The firm said it would hire 1,000 electronic and software engineers and 4,000 workers across other sectors, including manufacturing.
Most of the jobs will be based in the UK, with recruitment taking place over the coming year. The firm has five sites in the West Midlands, and one on Merseyside.
The carmaker, which is owned by India's Tata Motors, employs more than 40,000 people globally,
The company will build the I-PACE, in Austria. But it has indicated it would like to make such models in the UK if conditions such as support from government are met.
Jaguar Land Rover has indicated half of all new models will be available in an electric version by the end of the decade, necessitating new skills among its staff.

The 26-year-old is expected to play five games for the Sixers before joining up with England's limited-overs squad in India.
"To get the opportunity to play at the SCG is obviously a massive ambition of mine," he told the club website.
Roy could make his debut in the game against Sydney Thunder on 20 December.
He played three Big Bash games for Thunder two seasons ago.
"Jason is known as an explosive weapon at the top of the order and we look forward to his contribution, bringing also his English experiences from which we can share," said Sixers head coach Greg Shipperd.
England begin the limited-overs section of their tour to India next month.
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She said, if the party was re-elected in May's Scottish Parliament election, it would introduce a more "progressive" local tax from April 2017.
The reforms could see councils given a share of income tax revenues in an effort to give them an "incentive" to boost economic growth.
Last year, a commission on reform called for a "more progressive" tax.
The Commission on Local Tax Reform did not recommend a single alternative but it suggested there could be merit in combining a property-based levy with an element of income tax.
The current council tax charges householders on the value of the property they live in. The rate it is charged at has been frozen by the Scottish government since 2007.
Speaking at the David Hume Institute in Edinburgh, Ms Sturgeon said: "The report from the cross-party Commission on Local Tax Reform made clear that now is the time to reform local taxation.
"The commission argued for measures which will make council tax more progressive, and which will give greater assistance to people on lower incomes.
"So next week we will set out details of how we intend to achieve this from April 2017 onwards.
"These changes will be part of a longer term plan to increase the accountability of local councils to the populations they serve."
Discussions with local authorities are expected to determine how the Scottish Parliament can gain more power over income tax and local authorities can secure a share of income tax revenues for their area.
Asked if councils should be given power over sales and tourism taxes, as recommended by the commission, Ms Sturgeon said priority would be given to the assignation of income tax and other council tax powers would be considered.
"Scotland is a small country and I think it is right that we take steps to incentivise local authorities to boost economic growth in their own areas, but equally I think we have got to be careful about creating a postcode lottery in terms of tax rates in different local authority areas."
Carmaker Jaguar Land Rover has teamed up with virtual band Gorillaz to find 5,000 staff to enhance its expertise in autonomous and electric technology.
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Surrey and England batsman Jason Roy has agreed a short-term deal to play for Sydney Sixers in the forthcoming Big Bash tournament in Australia.
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The SNP will set out details of its plans on council tax reform next week, First Minister Nicola Sturgeon said.