Hi,
Yes a few problems here
Another one, you say you have an input of plus and minus 5 volts and you want to increase that by a minimum of 3 fold which works out to plus and minus 15 volts, yet presently you only seem to have a 24vdc power supply which isnt enough. To get plus and minus 15 volts you need at least a 30 volt power supply or better yet a little higher than that like 34 volts, but better yet you should have plus and minus 16 volt power supplies as a min, and plus and minus 20 volt power supplies would be better.
When you amplify +5 volts by a factor of 3 you get +15 volts, and when you amplify -5 volts by same factor you get -15, so that would give you a max output signal of -15v to +15v which i guess is what you are after.
Seeing as you dont have the DC power supply available, would a 2x factor be good enough rather than a 3x factor? Because if not, you'll have to get a better DC power supply or else modify the one you have if possible to put out a plus and minus voltage. Plus and minus 24v instead of just plus 24 volts would be good.