switch mode power supply - Flyback Transformer core heating up

I am designing a Discontinous conduction mode flyback converter, 100kHz using UC3844 IC with the spec. 220V,50Hz to 5V 5A. The issue is that after testing it for an hour, the transformer starts heating up(tried with different cores).

Ambient Temp.: 27degC

Transformer Spec: 1st try: EE20/10/6 Core, 0.5mm Gap, Al=100nH/turns2(EE20/10/6 Datasheet)

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  Turns Ratio: 21 to keep Vds(max) Low

  
  


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  Primary: 1.7mH, 30 SWG, 130 turns, 1 strand

  
  
  


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  Secondary: 5-6uH, 6 turns, 30 SWG, 7strands(I know, the diameter that i used is very low but could fit only this in the winding area and the strands have to be increased, for testing purpose designed this)

  
  


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  Auxiliary: 52uH, 14 turns,30SWG, 1 strand.

  
  

With this configuration, the transformer was heating upto 80deg C in just 30 min.

Form the calculations for the core loss, it was coming to 170mW. But Copper Losses were huge

Primary: Irms=0.4A, Resistance_dc=(total length)*Res. per length, Rp=(7.6*4*130)*0.221 mOhm=873mOhm, P=0.4*0.4*0.873*1.5=0.2W.

Secondary: Irms=9A, R_dc=(7.6*4*6/5)*0.221=8mOhm, P=9*9*.008*1.5=0.972W(This is the prob)

Seeing this with the thermal resistivity of 50K/W. Temp. would rise to almost 80 degC. So, it confirms with the problem.

Since i could not fit more dia. winding in this bobbin. Therefore, had to increase the core size.

2nd try: EE25/13/7 0.2mm gap Al=290nH/turns2 EE25/13/7

Same Inductance Parameters.

Primary: 77turns, 30 SWG, 1strand Secondary: 22SWG, 5 strand, 4turns.

But even then it is still rising to 65-70degC.

Currently working at 78% efficiency. What is happening in this case? Are my previous calculations correct? Is it because ac resistance has increased due to skin effect since operating at 100 Khz because of 22SWG wire? or something else?

Edit:

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3rd Try:

EE25/13/7 core: 0.4mm Gap, 187nH/turns2[earlier(340nh/turns2)]

Primary: 30SWG, 1 strand, 95 turns, 1.6mH

Secondary: 22SWG, 5strand, 5 turns, 5.2mH

Auxiliary: 35 SWG, 1 strand, 16turns.

Although the temp decreased but still hovering till 65degC.

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Circuit Diagram: