Role of repetition in Central Limit Theory

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What is the role of repetitions in Central Limit theory? If anyone can explain, intuitively and mathematically. Please refer to the image where one sampling distribution is with 5 reps and another one is with 10K

Std error of mean doesnt get affected i guess since SE = SD/sqrt(n) where n is sample size. Everywhere it is mentioned that n should be large enough.

Sampling repetition and distribution of means

the pic is generated using http://onlinestatbook.com/stat_sim/sampling_dist/