Yeah, it is possible. There are a couple of dozen better ways, but what you say could be built by someone with no knowledge of compression.
The key concept is compression ratios. If you divide the discharge pressure (in absolute units) by the suction pressure (in absolute units) then you get the compression ratios. I'll assume that your 1 atm suction is atmospheric pressure (let's call it 13 psia) and your 5 atm is 5 bar(a) or 72.5 psia. That is 5.5 compression ratios. For design purposes reciprocating compressors are generally limited to 4.5 ratios, but let's say you have a liquid cooled cylinder like a Compressco or an Ajax so 5.5 ratios is ok. Now you are taking your 72.5 psia gas to 145 psia which is 2.0 compression ratios. A cake walk for a recip. A more reasonable design might be 13 psia to 44.2 psia (3.4 ratios) and then 42.6 psia to 145 psia (another 3.4 ratios).
A dozen different manufacturers make a 2 stage compressor with the ability to use an inter-stage and after cooler with a single driver. Not a big deal, you really don't need two separate compressors.
David
