Context: This line is the turning point of the Flood, right before the rain stops.
Context: The people of Israel were working as slaves in Egypt and cried out.
Context: After telling us all the bad things that will (G-d forbid) befall us if we do not follow G-d's commandments, we learn that if we clear our hearts then G-d will forgive us.
Context: This Psalm talks about how wonderful G-d is.
(5) He hath given food unto them that fear Him; He will ever be mindful of His covenant.
Context: Next line of the previous one.
Context: This Psalm describes in detail how we repeatedly rebelled against G-d and were punished but goes on to say that G-d always remembers the covenant and relents.
Context: G-d is reminiscing about our previous closeness and wondering what changed.
(60) Nevertheless I will remember My covenant with thee in the days of thy youth, and I will establish unto thee an everlasting covenant.
Context: G-d recalls how we went astray and violated the covenant and were punished in return.
Context: We are reassured that G-d will bring us back to the land and we will be happy there.
Context: In this continuation of the section quoted earlier (third verse, above), we hear that G-d will not break the covenant, even if (when) we do.