how do we tell if ばかり means “about” or “only” ?

Question

If ばかり could mean approximately; about; and could also mean only; merely; nothing but;, then how should we know if this sentence ５０００円ばかりもっている。 means:

1) I have about 5000 yen.

or 2) I have only 5000 yen.

Answer 1

1. ばかり after an amount or a quantity means 'approximately', 'about':

   ５０００円ばかりもっている。→ I have about 5,000 yen.

   僕はここ３年ばかりあの人に会わない。→ I haven't seen him for about three years.

2. The sense of 'only', 'just' works after a verb:

   列車はたった今ついたばかりです。→ The train has just arrived here.

   or a noun/pronoun (not indicating a quantity):

   あの人は勉強 ばかりしていて... → All he does is study

Note that ばかりに, ばかりか etc. also exist and work differently.

As @Scott just pointed out, in your example, you would use だけ or しか (+negative) to mean "only".

Answer 2

If the verb is past tense it means "just" happened. If the verb is -te iru it means only.

There are about 3 or 4 other uses that arent used as much. bakarini nado...

×　５０００円ばかりもっている。 doesnt sound right.

○　５０００円だけ持ってる

○　５０００円しか持ってない