Selecting a switching transistor for a 5V relay
You probably don't want to run in the active region, because the transistor voltage will mean that the relay sees less than 5 volts, so you will have to get the transistor saturated.  Using the MMPQ3904 as an example, it lists VCE(sat) as 0.2 volts for IC = 10 mA and IB = 1mA, and 0.3 volts for IC = 50 mA and IB = 5mA.  To get the transistor saturate with an IC of 28 mA, you can extrapolate to about 2.8 mA per relay switch, and realize that your transistor will have a VCE of around .25 volts, leaving 4.75 for your relay.  Your transistor base voltage will be around 0.7 volts.  Look at your IC output spec, and design such that the IC's output resistance and voltage can provide 3 mA to a load of R2 in series with a diode drop.  Be sure your relay will work with 4.75 volts, and that your processor can deliver a total of 24 mA to the 8 transistor bases.  Otherwise, find an N-channel enhancement MOSFET with a low on resistance and appropriate VGS(th).  This will provide the same functionality with negligible processor current and voltage drop on the relay.