The verb in Philippians 2:5 is second person plural so that the verse says "Let this mind be in you (pl)" as opposed to "Let this mind be in you (sg)" The verse isn't saying that we must have the mind that was in Christ, but that we must put "this" into our minds, "this" being the humility that was in Christ Jesus.
The first two words of the sentence (τοῦτο φρονεῖτε - touto phroneite) simply translate as "Think about this" or "Set your minds on this." The plurality of the verb simply means that Paul is speaking to multiple people rather than just one. He's telling us all to set our minds on this. Unlike the 1 Corinthians passage, this verse isn't telling us that we have the same mind as Christ. Rather, it's telling us to fill our minds with humility.
The reason that's hard to get from the English translation is that the rest of the verse doesn't translate directly into English. A literal translation would look something like this:
Think about this in you, which also was in Christ Jesus
or, as the Lexham English Bible says:
Think this in/among yourselves which was also in Christ Jesus,
("among" is found in the footnotes)
Thus, this verse is not saying that the thing that should be in you, which was also in Christ Jesus, is the "mind" of Christ. Instead, it's saying that "this (τοῦτο - touto)," should be in you: Christ's humility (as elaborated by the next few verses)
As for why there's no article before "mind" in 1 Corinthians 2:16, I'm not entirely sure, but it is used a lot of other times without the article. For example, Rom 11:34 uses the same phrase as this verse in referring to the mind of the Lord (without the article) as incomprehensible and perfect. Also Phil 4:7 says that the peace of God will guard our hearts and minds (without the article) in Christ Jesus. So, I would guess that there's not much significance in it, but maybe someone can answer that better.
