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Z80Golf, $12345 (12 bytes)

00000000: 0605 3e24 ffc6 0c3c ff10 fc76            ..>$...<...v

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Assembly:

ld b, 5 ; loop 5 times
ld a, 24h ; '$' char
rst 38h
add 0Ch ; 30h='0' char
loop:
	inc a
	rst 38h ; putchar
	djnz loop
halt