@Polyanna can we have a few pictures please. I'm sure there is a cheaper option but it depends on what you really want. I'm guessing you want to go indexed shifting (one click, change gear). Might also mean you need to change your rear derallieur.
Modern shifters will probably be 8 speed so means you could over shift. Not tried this myself but I. Sure someone has used 7/8 speed shifters with 5/6 speed rear gears.
Riding position will change dramatically going from drop to flat bars. Again personal choice but you may loose some of the excitement.
I think I have a 5 speed indexed thumb shifter somewhere but not the corresponding left thumb shifter. It shouldn't be too hard to fit but again there are options to think about with the cabling. Some older bikes that had stem shifters also had cable holders where your current dt shifters are. Without them you will need to route a full outer cable possibly to your rear derallieur which can look messy.
Here's a picture of what I mean.
Hope this isn't too confusing but please ask for clarification as were all here to help.