Assuming the board will fit, not much else.
Upgrading an OEM PC with an aftermarket motherboard can be risky. Some OEMs like to use proprietary hardware and connectors. This may require manually rewiring things like front panel connectors and fan headers. If they used a standard motherboard, then it should be a one for one replacement.
Be prepared to have to re-purchase Windows though. If you can register your copy of Windows via an e-mail address (Windows 10). Otherwise the license key is tied to the motherboard and can't be re-used. Fresh installation of Windows may be needed to get rid of driver related issues when swapping motherboards. Sometimes it works though to just drop the OS onto new hardware.
On upgrades such as these I usually recommended getting your own computer chassis at the same time. Slightly reduces the workload to not have to take the old motherboard out and you then have a chassis more suitable for future upgrades. (If that is a concern anyway)
That said, an i5-2500k really pairs best with P67 or Z77 motherboards so that you can overclock. If you don't plan on that the H61 is an okay choice.