That is a nice looking bike and I can't see why getting the shifters to work properly should be much of an issue as they are friction and the set up is pretty easy.

But if you want to go ss...

Remove the shifters and derailers, true up the back wheel, and swap the 5 speed freewheel for a 16 tooth single (with a 3/32 pitch) and run the chain on the the inner ring if it's a 42.

Your gearing will be 65-67 gear inches and this is a nice all around gearing.

Just remember not to do anything stupid to such a nice looking bike as it is worth far more as an original than a conversion.

I can do a job like this in 30-40 minutes.

If the bike is French threaded and you want to do more stuff it gets a little more complex.