Your processor supports up to 3 monitors. What is really important here is your motherboard, and how they have implemented support for monitors.
https://ark.intel.com/products/97147/Intel-Core-i5-7400-Processor-6M-Cache-up-to-3_50-GHz Intel® Core™ i5-7400 Processor (6M Cache, up to 3.50 GHz) Product Specifications
It is very likely that your motherboard (if a desktop board), supports two, and perhaps three monitors. You do not have to install an nvidia or amd-based graphics card, unless you want to (perhaps for performance or gaming reasons).
So, just plug your monitor into your motherboard and you should be ok.
To answer this question better, we would need to know the manufacturer and model number of your board. Better yet, contact the manufacturer of the board for better support.
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