How can I connect two different DC power sources together?
You can connect them in series to add the voltages, but the resulting current capability will be the lower of the two current ratings.  Think of it like tying a 5 foot and 15 foot rope together.  You get a 20 foot rope, but its strength is whatever the strength of the weaker rope is.

No, you can't put two supplies together in any way to add both their current rating and their voltage.  This should be clear just from the power output alone.  The 15 V 5 A supply can deliver 75 W.  The 5 V 2 A supply can deliver 10 W.  Both together therefore can't deliver more than 85 W.  However, 20 V at 7 A would be 140 W.  That's a free lunch physics won't let you have.