Can I connect iMac(2014) to my MacBook Pro for sharing screen?

There are workaround products that might let you use that 27" iMac as a display. Neither would be as good as a hardware connection to a standalone Apple 27" 5K Studio Display .

One is DuetDisplay – "subscription" software. (You have to keep paying to use your display!). I don't believe it supports the full 5K resolution of your 27" iMac.

The other is Luna Display, from Astropad. If you understand its limitations and are sure that they would not be a deal-breaker for your particular use, this is, as far as I know, the only game in town for reusing that 27" 5K iMac display as a 27" 5K display. You would need to buy the USB-C version of the Luna Display "dongle" and plug it directly into your MacBook Pro. You would also want to run a USB or Thunderbolt connection between the two Macs to help carry video data. Even then the 5K refresh rate would probably be limited to 30 Hz or 45 Hz, and there might be temporary pixellation and lags.

That would make the arrangement most suitable for relatively static content, as Astropad acknowledges.

Astropad – Luna Display

Astropad – Use Your iMac as a Monitor: A Step-by-Step Guide [2024]

"Like any product, Luna Display does have limitations and it’s not recommended for high-motion content. For example, I wouldn’t recommend using Luna Display for gaming or video editing."

It sounds like you are trying to use Target Display Mode. That won't work.

Your iMac – the first 27" Retina 5K iMac – does not support Target Display Mode. Target Display Mode went away when that iMac came out, and no iMac (Retina or otherwise) ever had it again.

Apple also placed restrictions on the video source. Your 2017 MacBook Pro is old enough to support using a iMac that supports Target Display Mode as a TDM. But not when running Big Sur. You'd have to find an older iMac (one without a nice 27" 5K Retina screen) to use as the Target Display – and downgrade your MBP to Catalina or lower.

Read the bad news here: Use your iMac as a display with target display mode - Apple Support

All 2017 MacBook Pros can be upgraded as far as Ventura – but no further. You may want to upgrade to Ventura. There isn't much advantage to sticking with Big Sur – it won't run 32-bit applications, and it also isn't one of the "most recent three" supported by vendors like Microsoft and Adobe. After Sequoia comes out later this year, the most recent three will be (Ventura, Sonoma, Sequoia). So if you upgrade your 2017 MBP to Ventura now, you will have a year or so before Ventura, too, falls off the "most recent three" list. But upgrading to Ventura rather than downgrading to Catalina or easier means no support for using any iMac as a Target Display.

To upgrade to Ventura, back up your 2017 MBP, then see: How to download and install macOS - Apple Support .

I hope you didn't run out and buy a $50 Apple Thunderbolt 3-to-2 adapter and a $30+ Thunderbolt 1/2 cable (the hardware you would have required to make a proper Thunderbolt connection). You could use that adapter / cable for (1) creating an IP networking link between the Macs ("Thunderbolt Bridge"), or (2) using one of the Macs as an external disk drive for the other. But not, in this case, for Target Display Mode.