I want to replace my old lever shifters (Shimano 515) with something a bit more modern. Can I do this without replacing the front and rear derailleurs. And which shifter would be a simple, and or equivalent replacement.
Shimano never made a derailleur or shifter called "515", as far as I can tell. Perhaps you mean "SIS"? SIS stands (I think) for Shimano Integrated Shifting, which is indexed shifting.
The fact that you've only got five cogs in back suggests that you've got an old, low-end bike. You might find that upgrading your shifters will exceed the total value of the bike. I also don't know whether Shimano's low-end derailleurs are compatible with their brifters for indexed shifting. I'd take it by a bike shop and ask for an opinion.
I expect you will be wanting to move from downtube friction shifters to bar-mounted indexed shifters. Is your bike MTB or road?
If road you might want brifters. These can be very expensive so first assess whether it's worth it. You'll need to select shifters that have the same number of clicks as your chainring & cassette. Also, you'll need to make sure the index spacing for your shifters is compatible with your deraileurs and gears. See this Sheldon article for more info
If what you currently have are friction shifters then almost certainly your sprockets are not designed for indexed shifting. Converting to "indexed" shifters will not give you indexed shifting, only lousy, unreliable shifting.
To convert a non-indexed bike to indexed you'd need to replace the sprockets. Replacing the rear (if you can find a compatible replacement) would be relatively inexpensive, but replacing the front (which would probably involve replacing the crank) might very well cost more than the bike is worth.
(However, if your setup is actually "SIS", then you should already have indexed shifters, and you "only" need to be sure that the new set is compatible with the old in terms of cable distance traveled per gear.)
You only need to replace the shifters, but make sure to look for a model that has the same number of gears in the front and back. When you shift, the indexing happens inside the shifter, not the derailleur. Derailleurs are compatible with all speeds, and even friction shifters. All you have to do to replace them, is get a shifter with the matching number of gears on your bike.