Nisaa
No. During hayd a woman does not perform salah, whether obligatory or voluntary, and this is one of the few points in this area where all four madhabs agree without exception.
The ruling rests on the hadith of Fatimah bint Abi Hubaysh (Radi'Allahu Anha). The Prophet (Salla Allahu 'Alayhi Wa Sallam) told her: "When it is menstrual blood it is dark and recognizable, so when it is like that, then stop praying, and when it is otherwise, do wudu and pray, for that is from a vein." (Narrated by Abu Dawud and al-Nasai; classed as sahih by Ibn Hibban and al-Hakim). The instruction is explicit: once the blood is hayd, prayer stops. Elsewhere the Prophet (Salla Allahu 'Alayhi Wa Sallam) asked, as a settled matter rather than a real question, "Isn't it true that a woman can neither pray nor fast during her menses?" (Narrated by al-Bukhari), naming prayer and fasting together as the two acts hayd suspends.
She does not make it up afterward
This is the detail that surprises people who already know the fasting rule, because the two obligations are not treated the same. 'Aishah (Radi'Allahu Anha) said: "When we would have our menses during the lifetime of the Prophet (Salla Allahu 'Alayhi Wa Sallam), we were ordered to make up the days of fasting that we had missed but were not ordered to make up the prayers that we had missed." (Narrated by al-Bukhari). Fasts missed for hayd are made up later; prayers missed for hayd are not made up at all, and every madhab holds this. A woman does not owe five extra rak'ahs for every day she bled.
Why the two are treated differently
Scholars explain the gap by the weight each obligation carries. Fasting comes once a year, and the missed days are few enough to make up. Prayer repeats five times a day, and hayd can run to ten or fifteen days in a single cycle; requiring that many missed prayers to be made up on top of ordinary life would be a hardship the Shariah does not impose. The suspension of prayer during hayd is treated as a lifting of the obligation itself for that stretch of time, not merely a permitted delay.
What continues around it
The exemption is specific to hayd. Istihadah does not stop prayer the way hayd does; a woman with irregular bleeding prays as normal, with a wudu-and-pad routine before each prayer. And a woman does not lose her connection to Allah for the days salah is lifted: dhikr, dua, and other acts of worship stay open to her during her period.
On the day hayd ends, see which prayer to pray first, since purity arriving inside Asr or Isha raises its own question about the prayer before it. And once she is pure, ghusl comes before prayer resumes, the same full bath performed at the close of any period. Janabah is a shorter, different kind of pause: it closes prayer only until Ghusl, not until bleeding itself ends; see can you pray while in a state of Janabah for that distinction. Nifas carries this same suspension; see can you pray during nifas for how it applies to postpartum bleeding specifically.