1) To amplify signal by 20,use an inverting op-amp to get a gain of 20.(depends on what your signal is).You may need rail to rail op-amps
2) Is your signal going from (+15,-15)like a square pulse ???? If then use a comparator so that u get it to +15,0.
3) Now,bring it down from (+15,0) to (+5,0) by using a resistive divider(R,2R) or you can even use an op-amp.Your wish
P.S.:Specify your signal,its frequency,what was its initial amplitude before 20x gain.The above may not work if your signal frequency is very high.