88 TC Running Condition

[turboed88]

I just bought my first 2.3L Turbo Coupe 5 speed,its and '88,I don't know anything about these cars.The problem is:When I'm in neutral I can rev it in high RPMs,same goes for 1st and 2nd gear,but when i shift into 3rd,4th or 5th I can't pass 2,500Rpm.If I do it seems to shutter causing the the rpms to go low.But I can pass 2,500rpm if i give it gas very slowly and work my way up to speed.Not sure what to due.Does this mean it has a weak fuel pump or something?

 

[g_lower]

if it were my car I would start with the fuel filter, I have several of these cars they can be tricky to get figured out. where are you located?