Switch Working

If i have two computers one is having an ip of 192.168.2.20 and other one having
192.168.5.60 and i connect both of them through a normal switch ( e.g. D-LINK)
that only works at layer two.
So my question is that will they be able to transfer data between themselves.

it depends on its subnet. if you use the 255.255.0.0 you have 65535 address on the subnet (but i don't think you are going to use that,) no problem with the communication of the two.

but if you use the 255.255.255.0 you have 254 hosts in a subnet, limited from 192.168.2.1 to 192.168.2.254, there is no way for them to see the 192.168.5.x network without the help of a router.