These are sometimes hard to understand.

                          Birincilere beşer yüz lira dağıtılır.

´the first five´ or ´five hundred´?

Or maybe ´one hundred given to each group of five´?

Birinci = the one who comes first

Birinciler = the ones who come first

Birincilere = to the ones who come first

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beşer yüz lira  =  500 hundred liras  [ group of  500 tl] in other words; 

500 tl---> to first  first comer

500 tl - ---> to second first comer

500  tl---> to third  first comer

500 tl ---> to fourth first comer.. 

[500  tl --> to all first comer............... ]

Birincilere beşer yüz lira dağıtılır.

500 tl  is given to each first comer. 

in other words;

First comers are given 500 tl  each.

Yani , each first comer will take 500 tl.

Thank you, tunci. I wonder why it is so difficult: this was the alternative that seemed the least probable to me.

Old distributives have disappeared from many languages but in Turkish you see it now and then.

There is a catch here.

beşer yüz lira should be equal to

beşer (tane) yüz lira = 5 of 100TLs (possibly 5 of a baknote of 100TL) for each champion

beş yüzer lira = 500TLs for each champion

But in the end, it (the first one) is used with second one´s meaning. A wrong usage IMHO.

beş yüzer lira (lira is the unit of measure)

beşer (tane) yüz lira (yüz lira is the unit of measure)

I could imagine a slight difference in meaning here. The donator who says he gave beşer yüz lira to each doesn´t want to make it sound like it was a big sum of money.

Just a guess from me.

the distributive ek always comes to the adjective

sekizer kalem

ikişer ikişer gruplar

ikişerli gruplar

beşyüzer lira

i think you can say beşer yüz lira and beşyüzer lira both

notice that here "lira" is a noun and not a part of the adjective. adjective is beş yüz so it takes the ek