The relevant rule for the order of citation of detachable substituent prefixes in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows.
P-14.5 ALPHANUMERICAL ORDER
Alphanumerical order is used to establish the order of citation of detachable substituent prefixes (not the detachable saturation prefixes, hydro and dehydro), and the numbering of a chain, ring, or ring system when a choice is possible.
Alphanumerical order is applied as follows in organic nomenclature. Nonitalic Roman letters are considered first, unless used as locants or part of a compound or composite locant, for example, ‘N’ or ‘4a’ (see P-14.3), or in an isotopic descriptor. (…)
P-14.5.4 When two or more prefixes consist of identical Roman letters, priority for order of citation is given to the group that contains the lowest locant(s) at the first point of difference.
Therefore, the correct name for the compound that is shown in the question is
since the order is ‘ethenyl’ > ‘propenyl’ > ‘propynyl’ and ‘prop-1-en-1-yl’ > ‘prop-2-en-1-yl’.
The fact that ‘4-propenyl’ is lower than ‘5-propenyl’ is irrelevant.