The Op's translation is somewhat interpretive, so let me quote the NASB which is more literal for 1 Cor 7:1-7
1 Now concerning the things about which you wrote, it is good for a man not to touch a woman. 2 But because of immoralities, each
man is to have his own wife, and each woman is to have her own
husband. 3 The husband must fulfill his duty to his wife, and
likewise also the wife to her husband. 4 The wife does not have
authority over her own body, but the husband does; and likewise also
the husband does not have authority over his own body, but the wife
does. 5 Stop depriving one another, except by agreement for a
time, so that you may devote yourselves to prayer, and come together
again so that Satan will not tempt you because of your lack of
self-control. 6 But this I say by way of concession, not of
command. 7 Yet I wish that all men were even as I myself am.
However, each man has his own gift from God, one in this manner, and
another in that.
Verse 1:
Paul is simply recommending that people be unmarried (as per v7)
Verse 2:
... but then says that it is perfectly OK, even preferable for people to be married an thus fulfill our (sexual) desires in the way God intended
Verse 3:
Neither husband nor wife should arbitrarily deprive the other of sex. Ellicott comments: "In this verse the Apostle answers the scruples of those who already were married and who doubted whether they should continue so."
Verse 4:
This is a pivotal verse that tells us so many things, but the principle is - sex is always to be mutually agreed and neither partner can be either demanding nor depriving. In a marriage, both partners are to be equal. (For Paul's time this was an extremely radical idea!!)
Verse 5:
This is the crux of the OP's question. One should not conclude here that prayer and sex are mutually incompatible. Far from it. However, occasionally, some couples may mutually agree that they wish to abstain temporarily, for a special season of devotion and piety to God. However, this should be temporary and they must "come together" immediately afterward. Ellicott also observes:
Any such separation should be temporary, and with consent of both
parties. Even then it must not be from mere caprice, but for some
religious purpose, such as a special season of prayer. (See Exodus
19:15; 1 Samuel 21:4.) The alteration in the Greek text of the word
“give” into the present tense, so as to make the word “prayer” refer
to daily devotions, and not to special and exceptional seasons, and
the interpolation of the word “fasting”—not found in the older
MSS.—are a striking example of how the ascetic tendencies of a
particular ecclesiastical school of thought led to their “amending”
the sacred text so as to make it be in harmony with their own views,
instead of reverently regarding it as that by which those very views
should be corrected.
And come together again.—Better (as in the best MSS.), and be together
again. This is still an explanation of the purpose of the separation,
not to be a lasting one, but that we may again return to the state of
union.
Verse 6:
This verse confirms the comment above that sex and prayer/devotion are not incompatible. That is, it is not necessary to abstain when one feels the need for special devotion. However, neither is it prohibited so long as it is voluntary and temporary.
Verse 7:
Paul here claims the spiritual gift of celibacy which he readily recognizes that only few are given. He readily accept that not everyone can be single and has no difficulty with people being married.