92 auto Civic engine problems

Hi, ive just recently bought a 92 civic which has run up 156,000kms. Ive noticed wen driving the car, on D4 or D3, that wen it is time for the gears to change it struggles, the engine noise gets louder and the revs go up to 4000-5000rpms before it changes.

ive noticed that if you try hammering down the accelerator the revs just get higher without the car gearing up.

although it is terrible wen the car is initially started, 5-10 mins of driving, improves it significantly.

is there anything I can do to fix this problem? Perhaps the transmission fluids? Or is this normal for an older car

thanks in advance!