Air carrier at 5000 FT with DTW TRACON experienced TCAS RA; traffic was reported by ATC and sighted by the flight crew; reporter-questioning lack of ATC response after traffic was reported in sight.

Narrative

We had a near miss collision with a small aircraft at 5;000 FT Northwest of Salem VOR at about 15 NM. We were instructed to maintain 5;000 FT in a high traffic area. ATC informed us of an aircraft at our 10 o'clock position traveling; in my opinion; southeast. TCAS showed the aircraft 300 FT below us. We were traveling 010 heading at this time. We spotted the traffic and reported it insight. ATC never responded. TCAS RA was to monitor vertical speed. Visual cue on VSI was not to descend. Then the aircraft made a left turn directly for us and began to climb. We followed RA to climb; and the aircraft flew directly below. I believe that the crew acted appropriately. ATC never responded to us at all. I believe he was under a heavier than normal workload. Three seconds later; the aircraft turned directly toward us; and we followed the TCAS Resolution to make an abrupt climb. I reported to ATC we were climbing. They said 'roger; maintain 7;000.' I repeated the instruction and no further actions were taken.