If the fixed income came from newly-printed money then yes, it would cause inflation. If it came from taxes then no, it would not cause inflation in and of itself.
In both cases, it would increase the purchasing power of the poor and reduce the purchasing power of the rich, because $5000 means more to somebody making $10000 than it does to somebody making $1000000.
In both cases, it would increase the purchasing power of the poor and reduce the purchasing power of the rich, because $5000 means more to somebody making $10000 than it does to somebody making $1000000.