Just as there's no such thing as "just i5", there's no such thing as "just Pentium III". There's various models of every series. The i5 has had various models for each of its microarchitectures. For example, right now the Intel Core i5 is in its 4th generation and is being produced according to the "Haswell" microarchitecture. Within this there's the i5-4430, i5-4670, i5-4670k, i5-4440, i5-4570, etc. All of these are cross-compatible and use the LGA 1150 socket (in other words, they all fit in the same motherboard), but let's go one iteration before.
The Ivy Bridge microarchitecture was used in the 3rd generation of i3, i5, and i7 CPUs. So for example, here there's the i5-3570k, the i5-3330, i5-3470, etc. All of these use the LGA 1155 socket which is distinct from the LGA 1150 socket that Haswell uses. Hence, the 4th generation and 3rd generation Intel Core i5's are not compatible with one another.
Similarly, the Pentium II series mostly used Socket Slot 1 while some of the Pentium III series used Socket Slot 1, others used Socket 370, and others used both. There are various Pentium III's from the Pentium III 450 up until the Pentium III 1400. It would be best to figure out which model it is. If you can't boot up the PC and find a System Information page to find out which Pentium III it is, then try to match them according to names or serial numbers you find on the physical CPU and on this Wikipedia listing:
http://en.wikipedia.org/wiki/List_of_Intel_Pentium_III_microprocessors