The word phileo, which is also used to mean kiss, does imply a sense of nearness and proximity. In Jn 5:20 the use of phileo fits well with the context of the passage, which details the unique relationship between the Father and the Son. The proximity in their relationship contrasts with the distance that exists between God and man because of sin (Is 59:2). Moreover, man cannot close that distance on his own. Thus men are not commanded to love God in the phileo sense.
W E Vine - phileo (φιλέω, 5368) is to be distinguished from agapao in this, that phileo more nearly represents “tender affection.” The two words are used for the “love” of the Father for the Son, John 3:35 (No. 1), and 5:20 (No. 2); for the believer, 14:21 (No. 1) and 16:27 (No. 2); both, of Christ’s “love” for a certain disciple, 13:23 (No. 1), and 20:2 (No. 2). Yet the distinction between the two verbs remains, and they are never used indiscriminately in the same passage; if each is used with reference to the same objects, as just mentioned, each word retains its distinctive and essential character. Phileo is never used in a command to men to “love” God.
In Jn 5:20 the use of phileo fits well with the context of the passage, which details the unique relationship between the Father and the Son. The proximity in their relationship contrasts with the distance that exists between God and man because of sin (Is 59:2). Furthermore, man cannot close that distance on his own. ThusBecause men are not commandedunable to love God in the phileo sense. Because men cannotdo so, the Son was sent to bridge the gap between God and man (cf 1 Pet 3:18, Eph 2:18-19).
For the Father Himself loves you, because you have loved Me and have believed that I came forth from the Father – Jn 16:27
“In this passage does Jesus use φιλέω to imply equality with His Father which would not be present if He had used ἀγαπάω?”
While the word φιλέω implies proximity and not necessarily equality, the proximity inherent in the very nature of the relationship that Jesus claimed to have with God the Father was understood by Jesus’ opponents to signify a claim to equality.
For this reason therefore the Jews were seeking all the more to kill Him, because He not only was breaking the Sabbath, but also was calling God His own Father, making Himself equal with God. – Jn 5:18
While the answer to the OP’s question is not clear, the significance of φιλέω lies in how it reinforces the proximity between the Father and the Son and what that proximity ultimately says about the Son’s identity. In my opinion, the word φιλέω reflects and amplifies that proximity in a way that ἀγαπάω would not.