Oracle 11g Release 2

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with t as
(
select '{{Property1 {property1_string}} {Property2 {property2_string}} {Property3 {property3_string}} {Property4 {property4_string}} {Property5 {property5_string}}}' s FROM DUAL
)
select REGEXP_SUBSTR(s,'[^{} ]+', 1, 2 * 1) FROM t;

REGEXP_SUBSTR(S,'[^{}]+',1,2*1)

property1_string

with t as
(
select '{{Property1 {property1_string}} {Property2 {property2_string}} {Property3 {property3_string}} {Property4 {property4_string}} {Property5 {property5_string}}}' s FROM DUAL
)
select REGEXP_SUBSTR(s,'[^{} ]+', 1, 2 * 2) FROM t;

REGEXP_SUBSTR(S,'[^{}]+',1,2*2)

property2_string

with t as
(
select '{{Property1 {property1_string}} {Property2 {property2_string}} {Property3 {property3_string}} {Property4 {property4_string}} {Property5 {property5_string}}}' s FROM DUAL
)
select REGEXP_SUBSTR(s,'[^{} ]+', 1, 2 * 3) FROM t;

REGEXP_SUBSTR(S,'[^{}]+',1,2*3)

property3_string

with t as
(
select '{{Property1 {property1_string}} {Property2 {property2_string}} {Property3 {property3_string}} {Property4 {property4_string}} {Property5 {property5_string}}}' s FROM DUAL
)
select REGEXP_SUBSTR(s,'[^{} ]+', 1, 2 * 4) FROM t;

REGEXP_SUBSTR(S,'[^{}]+',1,2*4)

property4_string